text:
Education in Uzbekistan/Introduction

Uzbekistan is a state of youth. Children, adolescents and young people under the age of 25 make up approximately 60% of the total population. The ancient heritage of Uzbekistan is characterized by love for children, concern for their health, well-being and education. At five million children are studying in school, and more than a million are preparing to become schoolchildren at the kindergarten level. The education of children and youth is one of the main priorities of the state policy of the country. That is why the law on education was adapted in June 1992, which became one of the first laws in our young sovereign state.

The essence of the education reform in Uzbekistan is to preserve the existing intellectual potential of the educational system and change our goals and actions in order to develop people capable of building and living in a democratic civil society and a free market economy. Since gaining independence, the people of Uzbekistan have realized their great responsibility as citizens of the international community and as citizens of our planet. Therefore, one of our main goals is to raise a healthy generation, both physically and mentally. The core principles of our new education policy support this endeavour. Our goals are defined as follows: humanistic, democratic methods of education and socialization, the priority of human values, national and cultural traditions, as well as the separation of educational institutions from the influence of political parties and social and political movements.

Currently, when transforming all social activity and development prospects of the country, textbooks are being updated, new subjects are being added, and retraining of teaching staff is being carried out. The development of new state educational standards is nearing completion. A large number of new types of schools are being created. These schools specialize in foreign languages, economics and environmental issues.

Along with this, research to continue the educational complex is being carried out, which includes a kindergarten, a secondary school, research and educational institutions.

Of course, all these processes are not simple. The government must solve many economic and social problems, in addition to other issues. With the support of half a million hardworking teachers who share the same vision, we hope to reach our goal. We understand that one of the main results of the educational reform is a change in the thinking of our people and society.

At the same time, we understand that by striving to create a new education system in accordance with world standards, we will succeed by sharing our knowledge and experience with developing countries, contributing to the world education system.

title: Education in Uzbekistan/Introduction


text:
Education in Uzbekistan/Preface

Education cannot be stereotypically attributed to an area of departmental or sectoral policy, but should be approached as a nationwide, strategically important issue. The initial significance of education for socio-economic development is defined at the governmental level: the system of lifelong education in Uzbekistan has all the conditions for the renovation of both traditional and innovative forms of education, developing life-long learning activities and becoming an integral part of everyday human life. Let us consider the stages of lifelong learning, established in Uzbekistan.

In the era of globalization, education becomes an essential component of economic development and the accumulation of national wealth. The high spiritual level of the population can organically create a legal culture, the ability of people to live and work in a democratic state, being aware of their rights and freedoms, and being able to use them in the interests of individuals, state and society. The state is interested in the development of the intellectual and spiritual potential of the country: about 35% of Uzbekistan’s population is aged 16 and more than 62% is under the age of 30. The government expenditures on education are considered to be the most important investment in the growth of national wealth: Uzbekistan annually spends 10-12% of GDP and 35% of the costs of the state budget on the development and reforming of the education system. The prestige of the pedagogical professions is increasing, and thus teachers’ salaries also increase, with the growth in wages of teachers and professors over the past 10 years being 1.5 times the average rate of wage increases in other sectors of the economy. At the heart of educational reform is the establishment of a sense of prestige of knowledge, education and high intelligence in society. Only people who are aware of the need for harmony in national and universal values and have the latest knowledge and intellectual capabilities as well as advanced technologies can achieve the strategic goals of development.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Education in Uzbekistan/Preface


text:
Algorithms/Preamble

This book aims to be an accessible introduction to the design and analysis of efficient algorithms. Throughout the book we will introduce only the most basic techniques and describe the rigorous mathematical methods needed to analyze them.

The topics covered include:

 * The divide and conquer technique.
 * The use of randomization in algorithms.
 * The general, but typically inefficient, backtracking technique.
 * Dynamic programming as an efficient optimization for some backtracking algorithms.
 * Greedy algorithms as an optimization of other kinds of backtracking algorithms.
 * Hill-climbing techniques, including network flow.

The goal of the book is to show you how you can methodically apply different techniques to your own algorithms to make them more efficient. While this book mostly highlights general techniques, some well-known algorithms are also looked at in depth. This book is written so it can be read from "cover to cover" in the length of a semester, where sections marked with a  may be skipped.

This book is a tutorial on techniques and is not a reference. For references we highly recommend the tomes by [Knuth] and [CLRS]. Additionally, sometimes the best insights come from the primary sources themselves (e.g. [Hoare]).

Why a Wikibook on Algorithms?
A is an undertaking similar to an open-source software project: A contributor creates content for the project to help others, for personal enrichment, or to accomplish something for the contributor's own work (e.g., lecture preparation).

An open book, just like an open program, requires time to complete, but it can benefit greatly from even modest contributions from readers. For example you can fix "bugs" in the text (where the bug might be typographic, expository, technical, aesthetic or otherwise) in order to make a better book. If you find an opportunity to fix a bug, simply click on "edit", make your changes, and click on save. Other contributors may review your changes to be sure they are appropriate for the book. If you are unsure, you can visit the discussion page and ask there. Use common sense.

If you would like to make bigger contributions, you can take a look at the sections or chapters that are too short or otherwise need more work and start writing! Be sure to skim the rest of the book first in order to avoid duplication of content. Additionally, you should read the Guidelines for Contributors page for consistency tips and advice.

Note that you don't need to contribute everything at once. You can mark sections as "TODO," with a description of what remains to be done, and perhaps someone else will finish those parts for you. Once all TODO items are finished, we'll have reached our First Edition!

This book is intentionally kept narrow-in-focus in order to make contributions easier (because then the end-goal is clearer). This book is part two of a series of three computer science textbooks on algorithms, starting with Data Structures and ending with Advanced Data Structures and Algorithms. If you would like to contribute a topic not already listed in any of the three books try putting it in the Advanced book, which is more eclectic in nature. Or, if you think the topic is fundamental, you can go to either the Algorithms discussion page or the Data Structures discussion page and make a proposal.

Additionally, implementations of the algorithms as an appendix are welcome.

title: Algorithms/Preamble


text: Algorithms/Appendix B: Sources

title: Algorithms/Appendix B: Sources


text:
User talk:Mr.True Heart.SL

Mr.True Heart.SL (discuss • contribs) 04:34, 25 February 2024 (UTC)this page is for publishing, short story and for creating series of story.Its being published by one writer. under every respective policy of wiki books.

title: User talk:Mr.True Heart.SL


text:
User talk:Icandostuff

Welcome!
Welcome, Icandostuff!

If you have any questions, you can ask in the assistance reading room or possibly contact me personally. MathXplore (discuss • contribs) 05:47, 25 February 2024 (UTC)

title: User talk:Icandostuff


text: Category:Book:Education in Uzbekistan

title: Category:Book:Education in Uzbekistan


text: Category:Book:Theory of Formal Languages, Automata, and Computation


text:
User talk:Jonashtand

Welcome!
Welcome, Jonashtand!

If you have any questions, you can ask in the assistance reading room or possibly contact me personally. MathXplore (discuss • contribs) 10:42, 25 February 2024 (UTC)

title: User talk:Jonashtand


text:
User:Mr.True Heart.SL

Under the Painted Sky
Once upon a time, in a cozy seaside town, there was a boy named Iyan. He loved spending his evenings watching the sunset from the cliffs. One day, as he admired the sky turning shades of pink and orange, he noticed a girl nearby. Her name was Lily, and she was painting the sunset with her colorful brushes.

Curious, Iyan approached her and struck up a conversation. They talked about their love for nature and the beauty of the ocean. As they watched the sun disappear into the horizon together, Iyan felt a warm feeling growing inside him. He realized he enjoyed Lily's company and hoped to spend more time with her. As they said goodbye for the evening, Iyan couldn't help but feel excited about the new friendship blooming between them. Little did he know, their meeting was the start of something beautiful, under the painted sky.

The next day, Iyan started his day joyfully a new change rises in him. He waited for the evening in eager, but this time the sun and time played with him. He feels every minutes as hours this day, Finally the sun showed mercy on Iyan, The evening came, he felt the sunset as a sunrise in this moment. He walked to the same cliff. He saw backside of lily. He gently says her name, lily looked back. Her wavy hair blocked the sea waves,

A gentle breeze calmed his heart, Her nose is a clear mountain, her eye brows showed the darkest color he ever seen, Her eyes showed a new realm, Her lip was a smooth cliff, After he saw her, He totally understand, Why god gave eyes to his life.

Lily asked Iyan to sit with her. Iyan also accepted her lovely invitation. They talked until the sun set. They improved the conversation with little touchings. The sensual evening embraced in their feelings. The conversation continues, Until the moon rises. They noticed the dark and walked back to their homes together. Iyan dropped lily on the way on her home. He also walked back to the home thinking about the nice conversation had with lily. He notices that that's not just friendship, its higher than that.

__NEWSECTIONLINK__

= Poems =  Conflict

Ashes of our literature
 In midnight's quiet - hundreds

 of screams are heard,

 Not from humans but,

''' From thousands of words. '''

 Blazes of fire curled,

 The pages of desire,

 The long road passes,

 The song of destruction,

 Many words vanished for,

''' vicious racists. Only ashes - remained '''

 Is this there glory?,

''' is this there weapon?. '''

Mr.True Heart.SL (discuss • contribs) 15:57, 2 March 2024 (UTC)

title: User:Mr.True Heart.SL


text:
User:Stockmausen/common.css

.vector-main-menu-action-opt-out { display: none; }
 * 1) bodyContent { text-align: justify; hyphens: auto; }

title: User:Stockmausen/common.css


text: Category:Bulgur recipes

title: Category:Bulgur recipes


text: Category:Chaat masala recipes

title: Category:Chaat masala recipes


text:
User talk:61.5.141.115

--Xania   talk 07:37, 26 February 2024 (UTC)

title: User talk:61.5.141.115


text:
User:Project Firecorn/GPT4All

This page is under construct. You are welcome to collaborate

GPT4All is an Open Source AI application to use and train chatbots.

It has a graphical user interface and a python API.

GUI
Installation

How to use

Python API
Basics

Training
Basics

title: User:Project Firecorn/GPT4All


text:
User:Project Firecorn/GPT4All: Installation

To install GPT4All go to https://gpt4all.io/index.html and choose your operating system.

System requirements
To-Do


text:
Cookbook:Panamanian Ropa Vieja

Ingredients

 * 2 lb flank steak, cut into large pieces
 * Salt
 * Sazón
 * Dried oregano
 * Garlic powder
 * Ground cumin
 * Black pepper
 * 1 can tomato paste
 * Chicken, vegetable, or beef broth
 * Good-quality dry white wine
 * Yellow or white onion, chopped
 * Green and red bell peppers, cubed
 * Carrots, sliced
 * 4–6 cloves of garlic, cut in quarters
 * ½ cup pitted green olives, sliced
 * Bay leaves
 * Cilantro

Procedure

 * 1) Season the beef with salt, sazón, cumin, oregano, garlic powder, and pepper, and coat well.
 * 2) Whisk together the tomato paste, wine, and broth in a medium bowl. If you’re cooking this dish on the stove, use 3 cups of broth—you’ll need more since some of it will evaporate on the stove.
 * 3) Sauté the vegetables:
 * 4) * If using an Instant Pot, set it to the sauté setting. Add the oil and then the onions, bell peppers, and garlic. Cook for 3–4 minutes until softened. Then press cancel.
 * 5) * If using the stove, sauté the vegetables in a large Dutch oven on medium-high heat.
 * 6) Nestle the meat into the onions so half are on the bottom and half are above the meat. Add the carrots, olives, bay leaves, and cilantro (if using). Pour the tomato mixture over everything.
 * 7) Cook:
 * 8) * If using an Instant Pot, put the lid on, and cook on high for 45 minutes. Once done, unplug the pot, and do a natural release.
 * 9) * If using the stove, bring the pot to a boil, cover, reduce the heat to low, and simmer until the meat easily shreds. It should take about 1½–2 hours. Add more water if it gets too dry.
 * 10) Shred the beef, discard the bay leaves, and top with more cilantro if desired.

title: Cookbook:Panamanian Ropa Vieja


text:
Linux Basics/Introduction

The primary author, Attila Kun(ottwiz), thought that there should be an easy to use Linux tutorial for those who learn it in a formal or informal educational setting, but have no idea what to do with Linux. Attila Kun(ottwiz) studied Linux Basics as a subject in the school year 2018/2019 in high school, so his previous versions has a date like "2019.03.16."

This wikibook is translated from the Hungarian version of Linux alapok and covers the basics of Linux systems. Of course there will be things that work differently in other distributions such as files, but it mostly reflects what is seen in common distributions of Linux.

The number of sources indicates that we should not start from one source, but we should dive deep in to see things clearly. We should seek after on the Internet that how the article reflects reality (we can test it under live/virtual system, and if we can, we should search that if it's right).

Any contributions to this book are more than welcome!

Acknowledgments
I'd like to give big thanks to thottee from the Hungarian PenguinPit Discord community who helped a lot creating the original document(it was originally created in LibreOffice but I didn't want to suffer with making of it if I need to edit it sometimes), Balázs Úr who supervised this document and corrected the errors, and Balázs Meskó who corrected the grammar mistakes.

title: Linux Basics/Introduction


text: Linux Basics/Sources

title: Linux Basics/Sources


text:
Minecraft Speedrunning/Introduction

Speedrunning is the art of completing a game in as little time as possible. Minecraft is a sandbox block building and survival game. This book fuses the two to act as a strategy guide to speedrunning Minecraft Java Edition.

In the 2010's both Minecraft and speedrunning gained massive popularity in the gaming community, and as a natural result Minecraft speedrunning gained popularity. Minecraft is almost unique among freeform games for having an ending, and as a result beating Minecraft is usually defined as defeating the final boss known as the Ender Dragon. (Minecraft has 2 more bosses, but they don’t count for the any% category, but they do count for the “all bosses” category)

title: Minecraft Speedrunning/Introduction


text:
OpenSCAD Tutorial/Introduction

About OpenSCAD
OpenSCAD is a solid 3D CAD modelling software that enables the creation of CAD models through a scripting file. The domain specific language designed for this purpose allows the creation of fully parametric models by combining and transforming available primitives as well as custom objects.

About this tutorial
This tutorial assumes zero programming or CAD knowledge and is designed to guide you step by step through examples and exercises that will quickly build your understanding and provide you with the right tools to create your own models. Emphasis is placed on parametric design principles that will allow you to rapidly modify your creations and build your own library of reusable and combinable models.

The majority of presented examples and solutions to exercises are available as separate OpenSCAD scripts here.

As of 29-11-2019 this tutorial as well as all accompanying material were completely developed as a Google Season of Docs project.

title: OpenSCAD Tutorial/Introduction


text: User talk:216.15.126.147

title: User talk:216.15.126.147


text: Category:Panamanian recipes

title: Category:Panamanian recipes


text:
Chess/Introduction

Chess is an ancient strategy game that originated in India. It is played by two individuals on an 8×8 grid. The objective is to maneuver one's pieces so as to trap the opposing king in "checkmate". This book will cover the basic pieces of chess, before going on to some more advanced topics.

The history of chess began in India during the Gupta Empire, where its early form in the 6th century CE was known as chaturanga, which translates as "four divisions of the military" – infantry, cavalry, elephants, and chariotry, represented by the pieces that would evolve into the modern pawn, knight, bishop, and rook, respectively.

In Sassanid Persia around 600 CE, the name became shatranj, and the rules were developed further. Shatranj was taken up by the Muslim world after the Islamic conquest of Persia, with the pieces largely retaining their Persian names. In Spanish, "shatranj" was rendered as ajedrez, in Portuguese as xadrez, and in Greek as zatrikion, but in the rest of Europe it was replaced by versions of the Persian shāh ("king").

title: Chess/Introduction


text:
Open Source Church/Introduction

This book will illustrate open source software, downloadable from Github, useful for managing a church or parish. In particular, the functions of the ChurchCRM program will be analysed. ChurchCRM is released under the MIT license and installable both in a web hosting equipped with apache, php, mysql, phpmyadmin or simply on your PC as a standalone application via XAMPP.

ChurchCRM allows you to record data of people, families and groups who attend the parish and for each of these categories to establish properties, roles and classifications. For example for persons the roles could be head of household, wife, child etc., classifications could be member, visitor, guest etc., while properties could be disabled (specifying the type of disability), needs (financial, loneliness, need for assistance, etc.) and resources (bricklayer, lawyer, engineer, etc.).

For families, by creating one, its members can be entered immediately as people and as properties, for example single parent, single mother, etc.

You can then create all the groups that you want, for example Singers of the Mass, Parish choir, elderly group, Caritas Listening Center, Caritas Food Bank, Hospitality in Church, Musicians, Volunteers - visits to the sick, Scouts etc. People can be placed in multiple groups or moved from one group to another. The properties of a group could be youth, senior etc.

As regards data and reports it is possible to make queries of any type in order to search, for example, for disabled people, with economic needs, who have some resources, who are head of household, spouses, members, visitors, etc. and send emails to selected people. Other features are deposit management, fundraising and event creation...

title: Open Source Church/Introduction


text:
User talk:36.85.218.109

February 2024
MathXplore (discuss • contribs) 05:04, 27 February 2024 (UTC)

title: User talk:36.85.218.109


text:
Wikijunior:Languages/Sambal

What writing system(s) does this language use?
Sambal and almost all of the languages in the Philippines are written using the Latin alphabet.

The Sambal alphabet includes all of the same letters we use in English, along with 'Ñ' (enye), which the Filipinos borrowed from the Spanish, and 'Ng', a digraph already available as a single character in Baybayin.

Where is this language spoken?
Sambal is a Sambalic language spoken primarily in the Zambal municipalities of Santa Cruz, Candelaria, Masinloc, Palauig, and Iba, in the Pangasinense municipality of Infanta, and areas of Pampanga in the boundary with Zambales in the Philippines; speakers can also be found in Panitian, Quezon, Palawan and Barangay Mandaragat or Buncag of Puerto Princesa. The speakers of the language are decreasing due to the fact that many of the speakers are shifting to Tagalog & Ilocano.

What is the history of this language?
Sambal is an Austronesian Language. It was thought that the Austronesian language came from Taiwan and migrated southwards through sailing. They first reached Batanes islands, by around 2200 BCE.

Soon after the Age of Contact came and the Philippines started trading with other people like Persians, Arabs, Malays, Indians, Japanese, and Chinese. The people who traded with the Filipinos also introduced their language and culture, and soon after the Filipinos started using words from their languages and dressed, ate, and lived like them.

The Spaniards came and introduced Spanish, taught the Filipinos Spanish, and soon after many Spanish words entered the Language. The Americans came and introduced English and encouraged the use of English, so English words also entered Sambal. Sambal therefore is one of the most diverse languages of the world, with Sanskrit, Malay, Javanese, ../Mandarin Chinese/, Nahuatl, Persian, ../Arabic/, ../Japanese/, ../Spanish/, and ../English/ loanwords.

title: Wikijunior:Languages/Sambal


text:
User:Emil9989

Page Name

Sydney Buses

Sydney Bus System

title: User:Emil9989


text:
User:Emil9989/Page Name

Bla bla i am writing hello everyone.

Woah so professional.
This is amazing. "Meow meow, meow meow meow! Meow meow.

- A distinguished cat This is cool. I can become a professional writer for wikibooks. i can't wait to tell Joe Biden about this. He'll be so proud of me.

title: User:Emil9989/Page Name


text:
User talk:217.13.133.2

February 2024
MathXplore (discuss • contribs) 12:46, 27 February 2024 (UTC)

title: User talk:217.13.133.2


text:
User talk:Jeffery Jurek

Welcome!
Welcome, Jeffery Jurek!

If you have any questions, you can ask in the assistance reading room or possibly contact me personally. Lionel Cristiano (discuss • contribs) 13:15, 27 February 2024 (UTC)

title: User talk:Jeffery Jurek


text:
User talk:2409:4064:2ECF:B892:7D02:8C59:F016:8A2

February 2024
MathXplore (discuss • contribs) 14:19, 27 February 2024 (UTC)


text:
User talk:Adamvialsmoore

Welcome!
Welcome, Adamvialsmoore!

If you have any questions, you can ask in the assistance reading room or possibly contact me personally. Lionel Cristiano (discuss • contribs) 14:27, 27 February 2024 (UTC)

title: User talk:Adamvialsmoore


text:
Talk:The Wikimedia movement/back cover

Last sentence
I am having trouble understanding what the author is saying here:
 * "A new specificity of the movement, which ultimately inspires the desire to imagine differently, a humanity confronted with the challenges of an ever-changing world."

Anyone? Ottawahitech (discuss • contribs) 16:37, 27 February 2024 (UTC)

title: Talk:The Wikimedia movement/back cover


text:
User:Ottawahitech/wikibooks diary

2024-02-27
I've been looking around here since 15 January 2024 trying to see if there is anything I can contribute to this wiki. I still don't understand how this place works. On the surface it appears that the only users who will find this wiki useful are those who want to publish a complete book about a specific topic. I have looked around for a bit and found a lot of old undeveloped skeletons. The exception so far is the cookbook where, I assume, contributors who are not not the original author can add their own recipes. But there are a lot of old, most likely outdated technical half-finished books about proprietary ware with authours who are no longer active.

Today I saw for the first time a banner (MediaWiki:Sitenotice) which shows up on all the pages that I visited: which is a good sign for me because I rarely get to see such banners on other wiki-projects, even when others seem to see them. I wonder why this one does not also show up in the Reading room/Bulletin Board
 * "The Wikibooks community is developing a policy on the use of generative AI. Please view the draft policy and provide feedback on its talk page."

Also today I discovered that the book The Wikimedia movement has had content in it sine 2024-02-05 that I did not see until today and I wonder why. I am pretty sure I have checked this page periodically since I started participating more frequently on 2024-01-15.

2024-03-01
When I first started editing here I tried to find a new book every day by clicking Random book (Navigation menu). Then I started finding books in the list of Recent changes. I wish it was easier to locate books through Browse.

Some interesting pages discovered by accident:

One of the things I am trying out here is actively using my watchlist, something I rarely do on other wikis. This wiki is different because it does not automatically add pages that I edit to my watchlist which, so far, is a pain. But we'll see how I feel about it as time goes on and I have accumulated lots of pages on m watchlist. note to self: check if this is something controlled through my preferences. Another I do different here is use visual edit whenever I can (also a pain, but hopefully will get better when I get used to it).
 * 1) MediaWiki:Sitenotice
 * 2) Field Guide/Birds/Falco peregrinus
 * 3) Horticulture/Chainsaws
 * 4) Transwiki:Civics
 * 5) Cookbook:Fried-brain Sandwich
 * 6) Diablo Canyon Nuclear Power Plant: The WikiBook
 * 7) How to Solve the Rubik's Cube

visual stability
One of the things I really like about Wikibooks is its visual stability (I need to find a term for this). Knowing where things are helps when trying to go through foreign language wikis. The English wikipedia and others have moved on to a different looking page.

When I log in at WB I see the same every time:

 * On my first horizontal line: Ottawahitech Alert (n1) Notices (n2) My discussion Sandbox Preferences Beta Watchlist Contributions Log out
 * My second horizontal line: User page Discussion Read Edit Edit source View history
 * on the vertical left bar I see:

Navigation menu

 * Main Page
 * Help
 * Browse
 * Cookbook
 * Wikijunior
 * Featured books
 * Recent changes
 * Donations
 * Random book
 * Using Wikibooks

Community

 * Reading room forum
 * Community portal
 * Bulletin Board
 * Help out!
 * Policies and guidelines

Tools

 * What links here
 * Related changes
 * User contributions
 * Logs
 * Mute preferences
 * View user groups
 * Upload file
 * Special pages
 * Page information
 * Get shortened URL
 * Download QR code

Sister projects

 * Wikipedia
 * Wikiversity
 * Wiktionary
 * Wikiquote
 * Wikisource
 * Wikinews
 * Wikivoyage
 * Commons
 * Wikidata
 * MediaWiki
 * Meta-Wiki

Languages
If I ever decide to write a book (I really don't think so right now), what would I write about? One thing that comes to mind which is not properly covered in any of the wmf-wikis (I think?) is a comparison between wmf-wiki and Yahoo Groups administration

2024-03-18
I just discovered Requests for comment/Global ban for Slowking4 (2) when I was following links posted by @MathXplore on another wiki which led me to the VP at ENWQ where an announcement of this meta RFC had been posted on March 14. Just curious why the same announcement was not posted here

2024-03-20 Happy birthday
Just received a happy birthday note from my calendar. Today is my fourth birthday at [https://en.wikiquote.org/w/index.php?title=Wikiquote:Village_pump&oldid=2760053#Would_this_be_the_correct_page_to_ask_how_to_make_amends_for_any_harm_we've_caused_Wikiquote? the English Wikiquote], sigh...

Note to self: fix the wiki link above

title: User:Ottawahitech/wikibooks diary


text: Category:Akamu paste recipes

title: Category:Akamu paste recipes


title: User:R1F4T/sandbox


text:
User talk:2603:8000:6202:D0C3:49A0:DD44:5F92:BE2C

February 2024
MathXplore (discuss • contribs) 07:08, 28 February 2024 (UTC)


text:
Talk:Mathematics of the Jewish Calendar/The four postponements of the New Year

"Four Gates"
I also thought (like this article) that the "four gates" refers to the four categories of years. However, I think this is a mistake. See https://judaism.stackexchange.com/a/136764/22122 in the comments for the evidence. The Four Gates refers to the four possible days that Rosh Hashanah can end up on. MikeR613 (discuss • contribs) 18:44, 28 February 2024 (UTC)


text:
Foundations of dynamics

What is dynamics?
dunamis and energeia are terms used by Aristotle, which are generally translated as power and actuality. dunamis is also translated as potential. energeia is associated with ergon, the act, or work.

Potential and actuality are inseparable. Everything that is actual is the actualization of a potential. Conversely, if there were no actuality, there would be no potential, since potential is always the potential to do something.

Dynamics is the science of potential and its actualization.

To exist is always to dance. The actualization of a potential is always a movement. Dynamics is therefore the science of movement and its causes.

What modern physicists call potential energy resembles what Aristotle called dunamis.

Power, according to modern physics, is closely associated with potential energy, because it is the amount of energy that can be supplied per unit of time.

Kinetic energy is the energy of moving masses. It resembles Aristotle’s energeia.

Forces are the causes of variations in the movement of masses. They resemble Aristotle's driving causes.

Dynamics, in the modern sense, is at the same time the science of the movement of masses, the science of energy, or power, in all its forms, and the science of forces.

Kinetic energy is more actual than potential energy because it is more visible, more manifest. But we can also say of potential energy that it is actual. Because to be actual, or simply to be, to exist, is always to be able to have an effect on other beings. A being that cannot have an effect on other beings cannot physically exist. A being's actual being is therefore defined by what it can do, by its potential. It is what it can do. It is its being, even if it hasn't done it yet, and even if it never will.

To be actual is to have potential. Potential is always the potential to have an effect on other actual beings, or on oneself. So potential is always the potential to have an effect on the potential of other beings, or on oneself.

Everything that exists has momentum
Everything that exists physically always has momentum.

Proof: what exists physically always acts on other beings which exist physically. A being that never acted on other physical beings would never have any effect and could never be observed. It would have no physical existence. When a being acts on another, it modifies its movement, therefore its momentum $$\mathbf{p}=m\mathbf{v}$$ for a body of mass $$m$$ and speed $$\mathbf{v}$$. But the total momentum is always conserved. If one body increases the momentum of another, it loses momentum. If one body decreases the momentum of another, it gains momentum. Therefore a body without momentum cannot act on another and cannot exist physically.

Having momentum is a necessary condition for physical existence. Physical quantities are therefore often defined from momentum, and particularly forces and energies:

 * A force is the rate of change of a momentum.

 * An energy is the work of a force on a path.

What is a force?
If a body is not subjected to any force, it retains its mass and its velocity vector, and therefore its momentum. Its movement is in a straight line at constant speed. It is a uniform rectilinear movement.

Newton's first law:

The movement of a body which is not subject to any force is uniform rectilinear.

It is a law of inertia of movement. The velocity vector does not vary if nothing makes it vary.

From this first law, we deduce that if the momentum of a body is not constant, then there exists a force that causes its momentum to vary.

The fundamental law of dynamics:

A force is the rate of change of a momentum.

$$\mathbf{F} = \frac{d\mathbf{p}}{dt}$$

where $$\mathbf{F}$$ is the force acting on a body of momentum $$\mathbf{p}$$.

Newtonian physics assumes that the mass of a body does not depend on its speed, but the theory of relativity does not. For speeds small compared to that of light, the variation in mass is negligible. If we neglect the variations of $$m$$ as a function of the speed $$\mathbf{v}$$, we obtain Newton's second law:

$$\mathbf{F} = m \mathbf{a}$$

where $$\mathbf{a} = \frac {d\mathbf{v}}{dt} $$ is the acceleration of a mass $$m$$ which experiences a force $$ \mathbf{F}$$.

What is energy?
We define energy from the work of forces: the energy gained or lost by a body is the work of the forces exerted on it. When a body moves against forces, it must give up energy. When a body is pushed by forces, it gains energy.

We can move a heavy object effortlessly on an ice rink, because we don't have to fight against the force of gravity. On the other hand, it takes a lot of effort to lift a heavy object vertically, because we have to oppose the force of gravity. In the first case, the force of gravity does not work, because the movement is horizontal. In the second case, the force of gravity works, because the movement is vertical.

The work W of a force f on a mobile moving in a straight line over a length d is equal to the scalar product of the force vector f and the displacement vector d:

W = f.d = f d cos $$\theta$$

where $$\theta$$ is the angle between the force vector f and the displacement vector d. f and d are the lengths of the vectors f and d.

We can consider with Newton that gravity is a force. We then understand that we must provide energy to lift a heavy body, because we must exert a force which works against the force of gravity. The force of gravity is vertical. It does not work for a horizontal movement because it is perpendicular to the movement, cos 90° = 0. The only energy that must be provided to move a heavy body horizontally is the work against the friction forces.

The work of the force of gravity $$m\mathbf{g}$$ on a mass $$m$$ which is raised from a height $$h$$ is

$$W=-mgh$$

If in W = f.d = f d cos $$\theta$$, $$\theta$$ > 90°, then cos $$ \theta$$ < 0 and W < 0. The work of the force has a negative value because it is the energy lost by a body that moves while fighting against the force. This lost energy can be the kinetic energy E = 1/2 mv2. The speed v decreases because the body is braked by the force. If $$\theta$$ < 90°, cos $$\theta$$ > 0 and W > 0. The work of the force has a positive value because it is the energy acquired by a body that moves by being pushed and accelerated by force.

In the international system of units of measurement (MKSA, meter, kilogram, second, Ampere), the unit of energy is the Joule (J). One Joule is the work required to move a body one meter against a force of one Newton (N).

1 J = 1 N. 1 m = 1 N.m

The force of gravity on the surface of the Earth is approximately equal to 9.8 N, almost 10 N. One Joule is therefore approximately the energy required to lift a 1 kg body ten centimeters.

The fundamental law of dynamics $$\mathbf{F} = \frac{d \mathbf{p}}{dt}$$ and the definition of energy from the work of a force teach where to find energy and how to appropriate it. Energy is where there are forces. To appropriate energy, it is enough to make the forces work. So $$\mathbf{F} = \frac{d \mathbf{p}}{dt}$$ gives us the secret of power. For example, we can find E = m c², the Einstein equation which revealed the power of the atom, from $$\mathbf{F } = \frac{d \mathbf{p}}{dt}$$.

The kinetic energy of a moving mass
Consider two masses $$m_1$$ and $$m_2$$ connected by a spring.

When compressed or stretched, the spring exerts two forces $$F_1$$ and $$F_2$$, one on $$m_1$$, the other on m_2. If the mass of the spring is negligible compared to the masses it connects then we always have $$F_1 = - F_2$$.

We assume that each mass is only subjected to the force of the spring and that they are released against each other, at rest, after having extended the spring:

(Animation)

According to the fundamental law of dynamics:

$$F_1 = \frac{dp_1}{dt}$$

where $$p_1 = m_1 v_1$$ is the momentum of $$m_1$$. $$v_1$$ is its speed.

The forces $$F_1$$ and $$F_2$$ on the masses $$m_1$$ and $$m_2$$ are always in the direction of movement. The work $$dW_1$$ of $$F_1$$ on $$m_1$$ for a small displacement $$dx_1$$ is

$$dW_1 = F_1 dx_1$$

The work $$W_1$$ of $$F_1$$ between two instants $$t_1$$ and $$t_2$$ is

$$W_1 = \int_{t_1}^{t_2} dW_1 = \int_{t_1}^{t_2} F_1 dx_1$$

The energy gained or lost by the mass $$m_1$$ is therefore

$$W_1 = \int_{t_1}^{t_2} F_1 \frac {d x_1}{dt} dt = \int_{t_1}^{t_2} F_1 v_1 dt $$

$$W_1 = \int_{t_1}^{t_2} m_1 \frac {d v_1}{dt} v_1 dt = \mathbf{[} \frac{1}{2} m_1 v_1^2\mathbf{]}_ {t_1}^{t_2}$$

$$E_c = \frac{1}{2} m v^2$$ is the kinetic energy of a mass $$m$$ which goes at the speed $$v$$.

When a force is exerted on a mass in the direction of its movement, it gives it kinetic energy by increasing its speed.

When a force is exerted on a mass in the opposite direction of its movement, it takes kinetic energy from it by slowing it down.

When a force is exerted on a mass in a direction perpendicular to its movement, the mass retains its kinetic energy, therefore the magnitude $$v$$ of its velocity vector $$\mathbf{v}$$.

Einstein understood that all energy has mass, even kinetic energy. So the mass of a body depends on its speed. The calculation above is not exact. The faster a body goes, the more its mass increases and the more difficult it becomes to accelerate it, because the acceleration given by a force is inversely proportional to the mass of the body on which it is exerted. A mass can never reach the speed of light because it would need infinite energy to do so.

A flywheel is a massive wheel that is rotated around its axis. Mass is put especially at the periphery because that's where it goes the fastest. If friction is low, a flywheel can maintain its rotational speed for a very long time. It thus functions as an energy reservoir, because it retains its kinetic energy of rotation.

The potential energy of a spring
A spring can serve as an energy reserve. For example, 16 mm cameras work without electricity and allow continuous filming for several minutes, simply with a spring, which is wound by the crank.

To extend or compress a spring, the two forces exerted on it are in the same direction as the movement of each of its ends, we must therefore transfer energy to the spring. We have to expend energy, so we have to make an effort to tension or compress a spring.

A spring of stiffness $$k$$ near its equilibrium position exerts two forces $$F_1 = -F$$ and $$F_2 = F$$ on each of the bodies, at its left and its right, which compress or extend it:

$$F = - k x$$

where $$x$$ measures the variation in length of the spring compared to its equilibrium length $$l_0$$. This is Hooke's law of elasticity. It is true for all solids, provided that they are little deformed by the forces exerted on them. Springs are designed to respect Hooke's law even if they are very deformed.

If $$dx_1$$ and $$dx_2$$ are small displacements of the ends of the spring, the work $$dW$$ that must be provided to compress or extend the spring is

$$dW= -F_1 dx_1 - F_2 dx_2 = -F(dx_2-dx_1)= -Fdx$$

$$ dx = dx_2 - dx_1$$ because $$x = x_2 - x_1 - l_0$$.

To extend or compress a spring over a length $$x$$, it is therefore necessary to provide it with energy

$$W = \int_0^x dW = -\int_0^x Fdx = \int_0^x k x$$ $$dx = \frac{1}{2} k x^2$$

$$E_p = \frac{1}{2} k x^2$$ is the elastic potential energy of a spring of stiffness $$k$$ where $$x is its variation in length relative to its equilibrium length.

The cohesive forces of matter are electric. Elastic potential energy is electrical potential energy. It is a difference in energy of the electric field produced by the electrons and the nuclei of the spring. When we compress or extend a spring, we increase the electric potential energy conserved in the electric field produced by its electrons and its nuclei.

Conservation of energy
When the spring sets the masses in motion, its elastic potential energy is transformed into the kinetic energy of the masses. When the movement of the masses compresses or extends the spring, their kinetic energy is transformed into elastic potential energy of the spring.

Let be the sum of the kinetic energies of the two masses and the elastic potential energy of the spring.

now

so

The total energy E shared between the spring and the two masses is therefore conserved.

The law of conservation of energy:

The amount of energy gained or lost by a physical system is always equal to the amount of energy it received or gave up to another physical system.

We can also state it:

When two physical systems transfer energy from one to the other, their total energy does not change.

Conservation of momentum
The momentum \mathbf{p} of a body is always the product of its mass m and its velocity \mathbf{v} :

Let p be the total momentum of the two masses m_1 and m_1:

So the total momentum of the two masses is conserved.

The force F_2 exerted by the mass m_1 on the mass m_2, via the spring, is equal and opposite to the force F_1 exerted by the mass m_2 on the mass m_1, if we neglect the mass of the spring. The action of m_1 on m_2 is equal and opposite to the reaction of m_2 on m_1. Conservation of total momentum is therefore equivalent to the equality of action and reaction.

The law of equality of action and reaction

If two bodies A and B interact, the force exerted by A on B is equal and opposite to the force exerted by B on A.

Theorem: we cannot go to the Moon by pulling on our boots.

Proof: the hands exert on the boots a force directed upwards exactly equal and opposite to the force exerted downwards by the boots on the hands. The sum of the two is zero and therefore cannot give an upward acceleration.

The law of equality of action and reaction is Newton's third law. It is strictly exact only if A and B are in contact. The two equal and opposite forces are then exerted at the same point, the point of contact. But if A and B are far apart, they cannot be instantly sensitive to variations in each other's movement, because there is no instantaneous action at a distance. Information and physical beings always move with finite speed, never with infinite speed.

The law of conservation of momentum is better than the law of equality of action and reaction, because it avoids the problem of instantaneous action at a distance:

The law of conservation of momentum:

The momentum gained or lost by a physical system is always equal to the momentum it received or gave up to another physical system.

We can also state it:

When two physical systems transfer momentum from one to the other, their total momentum does not change.

Angular momentum
A body which rotates on itself and which is not subject to any external force maintains its rotational movement. The axis and speed of rotation do not change. This is what happens to a spinning top if it is in free fall. The rotational inertia of their wheels balances bicycles in motion. A bicycle at rest falls, because there is no longer any rotational inertia.

Angular momentum is a rotational momentum. It is to constant rotational movement what momentum is to uniform rectilinear movement. Like momentum, it is always conserved in the absence of an external force. The angular momentum lost or gained by one body is always the angular momentum gained or lost by another body.

The laws of the gift of momentum and energy
A body cannot give more momentum, angular momentum and energy than it has. If it gives all its energy then it is no more, because its mass is energy.

To provide momentum and angular momentum, it must exert forces. To give energy, it must also exert forces, because variation in energy comes with variation in momentum.

When a force is perpendicular to the speed of a mass, it does not work. It varies the momentum vector, but not its length, so it does not increase the kinetic energy of the body on which it is exerted. The body that exerts this force varies the momentum without losing its energy.

The fundamental laws of physics determine the forces that bodies can exert on each other. They are therefore the laws of the gift of momentum, angular momentum and energy.

Energy and momentum of fields
A field is a physical quantity defined at each point in space-time.

There is no instant action at a distance. Two bodies far apart that interact always do so through a force field, where information is propagated at a finite speed, always equal to or less than that of light. For example, two masses linked by a spring interact through the pressure field in the spring. In a pressure field, information is propagated at the speed of sound.

Fundamental forces are the forces between particles. When a body A exerts a force F on a body B, F is the vector sum of all the forces exerted by a particle x on a particle y, for all the particles x of A and all the particles y of B.

The force fields between particles are the electromagnetic field, which exerts electric and magnetic forces on particles, and the nuclear force field, which explains the stability and instability of the nuclei of atoms. Radioactivity is the consequence of nuclear instability: unstable nuclei disintegrate spontaneously, without the slightest force being exerted to break them.

According to Newtonian physics, gravitation is a field of forces between all masses, but the speed of propagation of information is infinite, because the law of universal gravitation imposes instantaneous action at a distance. According to Einstein's theory of general relativity, gravitation is not a force, but a field of space-time distortions, where information can never propagate faster than light.

Like everything else that exists physically, force fields have energy, momentum, and angular momentum. When a force is exerted on a particle, it always varies its momentum, and it can also vary its energy and angular momentum. These variations are caused by transfers of momentum, energy and angular momentum between the field and the particle on which it acts.

The energy or momentum of a physical system is always the sum of the energies or momentum of the particles that constitute it plus the sum of the energies or momentum of the fields that these particles produce.

We often count the energy of the field by assigning potential energy to the particles on which it exerts its forces. For example, we attribute electric potential energy to an electrically charged body. It is the sum of the electrical potential energies of all its electrically charged particles. But this potential energy is not an energy carried by the particles, because it does not vary their mass. It is an energy of the electric field, localized in the space around the particles. Counting the potential energy of particles is only one way of counting the energy of the field they produce.

The energy of mass
A particle is restless if and only if there does not exist an inertial frame of reference where it is motionless.

A particle is with rest if and only if there exists an inertial frame of reference where it is motionless.

Particles with rest have rest mass.

Everything that exists physically has mass, because everything that exists physically has momentum. Restless particles have mass, like particles with rest, but they have no rest mass, because they have no rest.

Photons are restless particles. The mass of a photon is

where E is its energy, p its momentum and c the speed of light.

Even a mass at rest is the energy of a field, the field of force that gave it rest. The rest mass of a particle resembles the work of the force on a path that took it from no rest to rest. For an electrically neutral particle, this work is equal to

E = m_0 c^2

where m_0 is the rest mass of the particle.

For an electrically charged particle of rest mass m_0, we must add to the work of the force which gave it rest the energy of the electric field that it produces around it to obtain E = m_0 c^2$$.

Let $$m_n c^2$$ be the work of the force which gave a charged particle rest. Let $$m_C$$ be the mass of the Coulomb field produced by this charge if it were isolated.

$$m_0 = m_n + m_C$$

In general, we measure $$m_0$$, not $$m_n$$ and $$m_C$$ separately, because we cannot undress a charged particle and ask it to leave its Coulomb field in the locker room before measuring its mass $$m_n$$.

When an electrically charged particle and its antiparticle, an electron and a positron for example, are exactly superimposed, the electric field they produce together is equal to zero everywhere in space. The mass $$m$$ of the pair, if it were at rest, would therefore be

$$m = 2 m_n$$

because the energies $$m_C c^2$$ of the Coulomb field of a particle and its antiparticle are equal, and their rest masses $$m_0$$ too.

The minimum energy required to create a particle-antiparticle pair is equal to $$2 m_0$$ not $$2 m_n$$. When a pair is created, the difference $$m_0 - m_n$$ is the minimum kinetic energy of the particle or its antiparticle, for the pair to be created.

After being created, the electrically charged particle and its antiparticle move away from each other. They thus produce a dipolar electric field. They give energy to this field while losing part of their kinetic energy.

The kinetic energy $$E_c$$ of a particle is always the difference between its mass multiplied by c² and its rest mass multiplied by c² also:

$$E_c = (m-m_0)c^2$$

The kinetic energy of a particle depends on the frame of reference in which it is measured, and therefore its mass too.

The mass of a particle, including its kinetic energy, is always the energy of one or more fields, the energy of the field that put it at rest, if it is a particle with rest, plus the energy fields that it produces around it.

When we count the energy of a physical system, we must add up all the energies of the fields associated with it, including the force field that gives the particles rest. Particles do not exist without the fields that they produce or that produced them, because they are quanta of fields. There are only fields and their quanta, the particles.

The fundamental laws of physics are therefore always the laws of the gift of momentum, energy and angular momentum from one field to another field. When the kinetic energy of a charged particle is transformed into electric potential energy, the field that gives the particles their rest and their kinetic energy gives up part of its energy to the electromagnetic field.

The gift of kinetic energy
The mass of an electrically neutral body with rest is the mass of the field which gives it rest. It is the sum of its rest mass and the mass of its kinetic energy. When one mass gives up kinetic energy to another, it loses part of its mass. Part of the energy of the field which gives it rest is transferred to the field which gives rest to the other mass.

Let two equal masses $$m_1$$ and $$m_2$$, $$m_1 = m_2 = m$$, which bounce on each other with speeds $$ v_1 = v$$ and $$v_2 = - v$$ equal and opposite, measured in a reference frame R.

If the masses are perfectly elastic, they retain their kinetic energy after the rebound:

$$v_{1out} = - v_1$$

so

$$\frac{1}{2} m_1 {v_{1out}}^2 = \frac{1}{2} m_1 v_1^2$$

The same for $$m_2$$.

In a reference frame R' which goes at speed $$v$$ with respect to R, $$m_1$$ is initially at rest. After the rebound it gains a kinetic energy equal to $$\frac{1}{2} m_1 (2v)^2= 2 m v^2$$, given up by the mass $$m_2$$.

In a reference frame R" which goes at speed $$-v$$ with respect to R, $$m_2$$ is initially at rest. After the rebound it gains a kinetic energy equal to $$ 2 m v^2$$, given up by the mass $$m_1$$.

From the point of view of R', $$m_1$$ gives up kinetic energy to $$m_2$$. From the point of view of R", $$m_2$$ gives up kinetic energy to $$m_1$$. From the point of view of R, $$m_1$$ and m_2 each retain their kinetic energy. How is this possible?

Energy always has mass. Mass is always the mass of the quanta of a field. If particles move from A to B from the point of view of one frame, they move from A to B from the point of view of all frames, because the presence of a particle in A or in B does not depend on the point of view. So it seems that a transfer of kinetic energy cannot depend on a point of view.

Restless particles carry energy at the speed of light. Their energy $$E = pc$$ depends on the frame of reference, because their momentum $$p$$ depends on the frame of reference, by Doppler effect. When the two masses bounce off each other, there are two particle flows, one from $$m_1$$ to $$m_2$$, the other from $$m_2$$ to $$m_1$$. From the point of view of R, these energy flows are exactly equal. This is why the two masses each retain their kinetic energy. But from the point of view of R' or of R", these two flows do not transfer the same energy, because of the Doppler effect. The difference is the transfer of energy from one mass to the other.

The principle of least action
We can find the fundamental equations of the dynamics of all physical systems by reasoning with the following three principles:

 * Kinetic energy $$E_c$$ is expense per unit of time.

 * Interaction energy $$E_i$$ is income per unit of time.

 * All paths naturally followed by a physical system are paths of least loss or maximum gain, paths for which the difference between total revenues and total expenses is maximum.

A path AB followed by a physical system is a path of least loss if it is such that all mathematically possible paths from A to B have a higher loss. It is a path of maximum gain if it is such that all mathematically possible paths from A to B have a lower gain.

The difference $$E_c - E_i = L$$ is called the Lagrangian of the system. The integral $$\int_A^B L$$ $$dt = \int_A^B E_c$$ $$dt - \int_A^B E_i$$ $$dt= S$$ is called the action. It has the dimensions of energy multiplied by time. It is the analogue of a loss: total expenses minus total income. Its opposite $$-S$$ is the analogue of a gain. The principle of least loss, or maximum gain, is called the principle of least action.

Time is reversible. Nature does not differentiate between the past and the future.

Proof: if AB is a path of maximum gain, the same path BA taken in the opposite direction is also naturally possible, because it is a path of minimum loss.

This theorem is almost always true for the fundamental equations of microscopic motions. The arrow of time, from the past to the future, does not appear in these equations, but only in the equations of macroscopic movements given by statistical physics and thermodynamics.

The principle of least action does not impose that all naturally possible paths go towards increasing gains, since time is reversible, it only imposes that all naturally possible paths maximize gains or minimize losses.

We can find Newton's three fundamental laws from the principle of least action, provided that we choose the appropriate Lagrangian.

Consider a race from A to B between a hare and a tortoise. The tortoise moves forward at a constant speed while the hare stops to take a nap. To arrive at the same time as the tortoise, the hare must make up for lost time. So he arrives all out of breath while the turtle arrives calmly. We can calculate that the tortoise chose a path of least action for the Lagrangian $$L= E_c = \frac{1}{2} mv^2$$, while the hare did not minimize its losses. We thus find Newton's first law: in the absence of forces, movements are always uniform rectilinear. That there is no force is reflected by the absence of interaction energy in the Lagrangian.

Points A and B are points in configuration space. A configuration is defined by the positions of all the bodies that are part of the system. If there is a single moving point, the configuration space is real, three-dimensional space. If there are n moving points, the configuration space has 3n dimensions.

An optimal path is determined by two points A and B and by a delay to reach B starting from A. The path of least action is the optimal path among all the paths which have the same endpoints and the same delay. A is like a starting point at a fixed time and B is a meeting point, at an equally fixed time. The path of least action is the optimal path to arrive at the meeting place at the appointed time.

When we know the path of least action, we can calculate the speeds along the entire path, therefore the speeds at point A and point B. We therefore obtain a function between the final speed at B and the initial speed at A. We can thus calculate the final speed after a certain delay according to the initial speed. By making the delay tend towards zero, we thus find the rate of variation of the speeds of the points of the system, therefore the rate of variation of their quantities of movement, therefore the forces which are exerted on them.

title: Foundations of dynamics


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Kitchen Remodel/Countertop

Plywood base
The type of quartz countertop that we were planning to install required a plywood foundation. The thinner the countertop material, the more the manufacturers encourage you to have such a foundation. Since we didn't know the first thing about the specifics of a plywood installation, we hired an experienced craftsman who assisted us with most of it, until we fully understood the concept and could finish without help.

We used 5/8" (15 mm) plywood. The idea is to cover the entire surface that will have a countertop. The front edges of the plywood have to be aligned to the front edge of the cabinet frame (while the drawer fronts and doors are being ignored). That included, in our case, the recesses for the dishwasher and wine chiller and the bar surface. There were cut-outs for the sink, the faucet, the cooktop and for our pop-up outlet. We didn't drill holes yet for the soap dispensers and the button for the insinkerator, though.

The two edges which would get a waterfall had to be covered with plywood, too. However, at the edge of the bar peninsula we were planning a wrap-around (= countertop material both on the edge's outside and the inside) and therefore omitted the plywood where the wrap-around would go.

Another spot that needed special attention was the bar surface. Our bar is very wide (more than 9 ft. resp. 289 cm), and the countertop sales person had recommended us to add a good reinforcement to the plywood cover there. So we used a wood router to cut a number of long grooves into the plywood surface into which we mounted iron bars.

The very cool thing about having the plywood in place is that you can finish installing your drawers and shelves and doors, if you haven't done so yet, and you can start to fill those cabinets with your things. We also finished the installation of our sink and faucet and began to actually use the kitchen. We had been without one for more than four months. With no date set for the countertop installation (we were still waiting for a call back to get a date for the measurements), we didn't have another option anyway. The one major appliance though that we couldn't use yet, without a proper countertop, was the cooktop.

Countertop
The selection of a countertop material is a great opportunity to cut back on expenses if someone figures that they went over budget with their cabinets and appliances. Laminate countertops come in all sorts of designs today, some of them even looking more interesting and appealing than the pricey alternatives. And there are many other options, too. However, my family does weird stuff in the kitchen, like soldering or other works that you normally would do in a workshop, so we decided not to take risks and to buy a material that is really heat resistant and tough: engineered quartz. We reduced the costs a bit by picking a product that was on sale in one of our local home improvement stores.

My other criteria, besides a reasonable price, was that the material must be mostly white, but picks up the color of the cabinet fronts, too, so we were quite pleased to find a cost-effective product with gossamer grey structures in a white base. I prefer a fine pattern over a large-scale one, because if there ever occur any damages, they will hardly be noticeable. The white was important to me because I wanted these very large horizontal surfaces to brighten up our kitchen space, both during daytime, with natural light coming through the windows, and after dusk when the lights come into play that we installed directly above.

The home improvement store which sold us the product, with the installation work in the price included, delegates the job to local firms. We learned during this process that contractors who install countertops cover a huge range of different ways of working. When we bought our first countertop, in New York State, a decade ago, we had someone coming to our place and pulling a laser-operated gimmick out of a case. He finished the measuring within a few minutes, obviously creating a set of digital data which the would probably feed directly into their stone cutting device. Well, now, in California, we saw exactly the other end of the spectrum: the contractor didn't use laser technology or even a tape measure, but simply created a huge template, glued together from wooden strips. What can I say? Both methods worked out. More or less.

A few weeks later the crew came back, with the prepared countertop material, and installed it. At that point, we could offer them our own template with the exact positions of our soap dispensers and the button for the insinkerator.

The best advice that I can give to anybody who pays for a countertop installation is to closely monitor the work while it is being done. Our contractors for example didn't use a mechanic's level but eyeballed literally everything, with the result that one of our waterfalls is not quite vertical, but a fraction of a degree off; they also seemed not to care too much about installing the countertop edge in constant distance to the cabinet fronts. The latter is most likely the result of their method of measuring. The good news is that to an innocent viewer, those flaws are not perceptible at all.

By the way, our contractor offered to cut and to install a matching windowsill, too. We declined, since we wanted a wooden one, matching our shelves, but I still found this an interesting idea.

title: Kitchen Remodel/Countertop


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User talk:76.14.183.64

February 2024
We welcome and appreciate your contributions, but some of your recent edits had to be undone. Please see What is Wikibooks? to learn more about what contributions are beneficial to Wikibooks.Justarandomamerican (discuss • contribs) 02:16, 29 February 2024 (UTC)

title: User talk:76.14.183.64


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User talk:69.124.239.183

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title: User talk:69.124.239.183


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User talk:Swrpurna

You cannot edit indefinitely due to disruptive editing. You may appeal this action with a reasonable argument by adding the text below.

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title: User talk:Swrpurna


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User:יוני2023

Please do not contact me privately or publicly. I need mental satisfaction from the "freedoms" thanks.

נא לא ליצור עמי קשר בפרטי או בציבורי. צריכה נחת נפשית מ"החופשיות" תודה.

title: User:יוני2023


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Electricity and magnetism/Electrostatics

Electric forces can be produced simply by rubbing different materials together, such as hair on plastic. This creates equal and opposite electric charges on the two surfaces that have been rubbed. We can then observe the attraction of charges of opposite signs, and the repulsion of charges of the same sign:

Coulomb's law
''Two motionless electric charges exert an electric force on each other proportional to the product of their charges divided by the square of their distance. The two forces, that exerted by A on B and that exerted by B on A, are in the direction of the line which connects the centers of the two charges A and B. These two forces are attractive for charges of opposite signs and repulsive for charges of the same sign.''

A field is a physical quantity that can vary at every point in space at every instant. For example, temperature is a field. Coulomb's law says that a motionless electric charge $$q$$ permanently produces an electric force field $$\mathbf{E}$$ throughout space:

$$\mathbf{E}(\mathbf{r}) = k_e \frac{q}{r^2} \mathbf{\hat r}$$

where $$\mathbf{r}$$ is the vector which goes from the charge $$q$$ to the point considered, $$r$$ is its length, $$\mathbf {\hat r} = \mathbf{r}/r$$ is the unit length vector in the direction of $$\mathbf{r}$$ and $$k_e = \frac{1}{4 \pi \epsilon_0}$$ is a constant which depends on the choice of units of measurement.

The force $$\mathbf{F}$$ exerted by an electric field $$\mathbf{E}$$ on a charge $$q'$$ is $$\mathbf{ F} = q' \mathbf{E}$$

So the force exerted by a charge $$q$$ on a charge $$q'$$ is $$\frac{1}{4 \pi \epsilon_0} \frac{qq'}{ r^2} \mathbf{\hat r}$$

The field $$\mathbf{E}$$ is like a mathematical intermediary for calculating the force exerted by one charge on another. But it is much more than a simple mathematical intermediary. It has an autonomous existence. Maxwell showed that light is an electromagnetic wave, that is to say a movement of propagation of the electromagnetic field ($$\mathbf{E}$$, $$\mathbf{B}$$) of which the electric field $$\mathbf{E}$$ is a component.

The electric field on the surface of a positively charged sphere:

The force exerted by two charges on a third is the sum of the forces exerted separately by each of them. All the charges in the Universe produce together throughout space an electric field which is the sum of the fields produced separately by each of them.

The Coulomb force is mathematically similar to the gravitational force: two masses exert a gravitational force on each other proportional to the product of their masses divided by the square of their distance. But the gravitational force is always attractive, because there is no negative mass. On Earth, the weight of a body is the gravitational force that the Earth exerts on it.

According to the theory of relativity, there is no instantaneous interaction at a distance. A charge cannot therefore instantly exert the Coulomb force on another. The force propagation time must be taken into account. This is why Coulomb's law is only a law of electrostatics. It allows the forces between motionless charges to be correctly calculated.

The cohesion of matter is electrostatic
A tiny grain of salt

Each line represents a bond between two ions in a NaCl crystal (sodium chloride is common salt). The blue and green colors represent the two ion species. It is a centered cubic crystal. Each Na+ ion is surrounded by 8 close neighbors Cl-. Likewise, each Cl- ion is surrounded by 8 close neighbors Na+. Two nearby ions always have opposite charges, because opposite charges attract each other while charges of the same sign repel each other.

The force that explains the cohesion of solids, atoms and molecules is the Coulomb force. The cohesion of liquids is also caused in part by this electrostatic force, but because the atoms or molecules are in motion, electrodynamic forces can also come into play.

A hydrogen atom consists of one proton, zero, one or two neutrons, and one electron. A proton is a positive charge. An electron is a negative charge, equal but opposite. A neutron is neutral. The electron is linked to the proton by the Coulomb electric force. More generally, an atom consists of a nucleus surrounded by electrons. The charge of the nucleus is positive, equal but opposite to the total charge of the electrons.

When the hydrogen atom is in its ground state, the lowest energy state, the presence of the electron around a proton resembles a spherical cloud:

The proton is at the center. The cloud around represents the presence of the electron.

If the atom is excited, the presence of the electron can have various forms:

A molecule is an assembly of atoms. Electrons are like glue that binds nuclei together. Two positive charges repel each other, but two positive charges separated by a negative charge can attract each other.

An ion is an atom or molecule that has lost or gained one or more electrons. Since atoms and molecules are always electrically neutral, ions are always charged. An atom or molecule that has gained one or more electrons is a negative ion. An atom or molecule that has lost one or more electrons is a positive ion.

A solid is an assembly of atoms, molecules or ions, linked to each other by electrostatic force.

To break an ionic crystal, one must separate ions attracted by electric force:

The attractive forces between charges of opposite signs are greater than the repulsive forces between charges of the same sign. This difference makes all the materials cohesive.

The mass of the nuclei is approximately 5000 times greater than the mass of the electrons accompanying them, because the mass of a proton or neutron is approximately 2000 times that of an electron, and an atom always has the same number of protons and electrons, and a number of neutrons approximately equal to or a little greater than the number of protons (except ordinary hydrogen, which has no neutrons). Since almost all mass is carried by nuclei (made of protons and neutrons), it is more natural to say that electrons are a glue that binds nuclei than to say that nuclei are a glue that binds electrons.

Two point charges of opposite signs should attract each other until they come together. We can calculate that the energy it could provide by falling on each other in this way is infinite. But matter doesn't usually collapse on itself, and it never releases an infinite amount of energy. Bodies always have a lower energy state, which is their ground state. In this state, they cannot give up energy, because they have no lower energy state to go to. Atoms, molecules and ions are in their ground state or in excited states which have higher energy. The hotter a gas is, the more excited its atoms or molecules are. A solid is in an excited state unless its absolute temperature is zero Kelvin.

To explain why an electron from a hydrogen atom does not fall on the proton, or more generally why materials do not collapse on themselves, Coulomb's law is not enough, we need quantum physics.

What is electric voltage?
In steady state, the electric voltage is the difference in electric potential between two points. Its unit of measurement is the Volt (V).

What is potential?

To understand potential, we must understand the work of a force.

We can reason about the electric potential in the same way as about the gravitational potential.

We can move a heavy object effortlessly on an ice rink, because we don't have to fight against the force of gravity. On the other hand, it takes a lot of effort to lift a heavy object vertically, because we have to oppose the force of gravity. In the first case, the force of gravity does not work, because the movement is horizontal. In the second case, the force of gravity works, because the movement is vertical.

The work W of a force f on a mobile moving in a straight line over a length d is equal to the scalar product of the force vector f and the displacement vector d:

W = f.d = f d cos $$\theta$$

where $$\theta$$ is the angle between the force vector f and the displacement vector d. f and d are the lengths of the vectors f and d.

The force of gravity is vertical. It does not work for a horizontal displacement because cos 90° = 0. The work of the force of gravity $$m\mathbf{g}$$ on a mass $$m$$ that is raised from a height $$h$$ is

$$W=-mgh$$

The work of a force is energy. If $$\theta$$ > 90°, cos $$\theta$$ < 0 and W < 0. The work of the force has a negative value because it is the energy lost by a body that moves against the force. This lost energy can be the kinetic energy E = 1/2 mv2. The speed v decreases because the body is slowed down by the force. If $$\theta$$ < 90°, cos $$\theta$$ > 0 and W > 0. The work of the force has a positive value because it is the energy acquired by a body that moves by being pushed and accelerated by the force.

In the international system of units of measurement (MKSA, meter, kilogram, second, Ampere), the unit of energy is the Joule (J). One Joule is the work required to move a body one meter against a force of one Newton (N).

1 J = 1 N. 1 m = 1 N.m

The force of gravity on the surface of the Earth is approximately equal to 9.8 N, almost 10 N. One Joule is therefore approximately the energy required to lift a 1 kg body ten centimeters. When the trajectory of a mobile is a curved line, we calculate the work of a force by reasoning on broken lines which follow the curved trajectory. If the lengths of the segments are shorter and shorter, a broken line becomes more and more similar to the curved line it follows. We find the work of the force by taking the limit of the sum of the work on each segment, when the length of the segments tends to zero. The work of the force is the integral of the scalar product of the force and the displacement vector on the path followed.

By definition of the scalar product, the work of the force of gravity g on an inclined segment AB is equal to g(hA - hB) where hA - hB is the altitude difference between its two ends. Now the altitude difference between A and C is equal to the sum of the altitude differences between A and B and between B and C:

hA - hC = (hA - hB) + (hB - hC)

So the work of the force of gravity g on any path going from A to Z is always equal to g(hA - hZ). It only depends on the difference in altitude of the ends A and Z, not on the path which connects A to Z. We have thus proven in the particular case of the gravity field on the surface of the Earth:

Theorem: the work of the gravitational force does not depend on the path followed.

If we neglect friction, the kinetic energy of a mobile on a roller coaster is the work of the gravitational force from initial rest. It only depends on the height difference $$h$$, not on the path followed:

The work of a force can depend on the path followed. For example, the work of a friction force is greater as the path followed is longer.

When a force field is such that the work of the force between two points does not depend on the path followed, we can introduce a potential. It is defined by choosing a point of zero potential. The potential at each point in space is then defined by the work of the force on a standard body between this point and the point of zero potential. For the force of gravity, we take as a standard a body whose mass is equal to one. For electric force, the standard is a body whose electric charge is equal to one. The potential is well defined because the work of the force does not depend on the path followed.

Let WXY be the work of the force on a unit body moved from X to Y, VX the potential at point X and O a point of zero potential. By definition of V, VA = WAO and VB = WBO. So VA - VB = WAO - WBO. Or WAO = WAB + WBO. So VA - VB = WAB. The potential difference between two points is therefore always equal to the work of the force on a unit body displaced between these two points.

The electric voltage between two points is the work of the electric force on a unit of charge moved between these two points. In steady state, the work of the electric force does not depend on the path followed, this force therefore derives from a potential. The electric voltage is then a potential difference. It is for the electric force what the difference in altitude is for gravity.

The unit of electric charge is the Coulomb. One Volt (V) is one Joule (J) per Coulomb (C). This is the potential difference necessary to give a charge of one Coulomb an energy of one Joule.

1 V = 1 J/C

When an electric voltage is imposed across a metal wire, an electric current passes through the wire, which is a current of electrons. The electrons are accelerated by the electric force, but their average kinetic energy does not increase, because they are slowed down by the metal. They lose by heating the metal all the energy they gained, through the Joule effect. Electric light was invented by heating a metal wire carrying an electric current to white heat. The electrical resistance of a material measures its ability to slow down electrons or ions passing through it.

Potential energy
The gravitational potential energy of a body of mass $$m$$ located at the point $$X$$ is equal to $$m V_X$$ where $$V_X$$ > is the gravitational potential at point $$X$$. When a body is at rest, its energy is not visible, not actual, because its kinetic energy is zero. When a body at rest is released into free fall, its gravitational potential energy is transformed into kinetic energy. The energy was already present when the body was at rest, but it had not manifested itself, it was only potential. Its transformation into kinetic energy is an actualization of the potential.

For a body in free fall, released at rest, its kinetic energy at the end of the movement is the actualization of its gravitational potential energy, initially invisible. It is equal to the work of the force of gravity. So the work of force is the actualization of potential. Potential energy is the potential to cause a force to work. We have potential when we have a force that we can put to work.

Energy has many forms: kinetic energy $$\frac{1}{2} mv^2$$ is the energy of a mass $$m$$ due to its speed $$v$$. Heat is the kinetic energy of atoms and molecules. Gravity energy, electrical energy, and nuclear energy are potential energies that depend on gravitational, electrical, and nuclear forces, respectively. Chemical energy is the electrical energy of atoms and molecules. Light energy is the kinetic energy of photons, the particles of light.

The equation for kinetic energy $$E = \frac{1}{2} mv^2$$ is only a first approximation. A relativistic calculation, in accordance with Einstein's theory, gives a more precise result.

The transformation of gravitational potential energy into kinetic energy is an example of conservation of energy. The energy never disappears. When a body loses energy, it always gives it to another body, or it transforms it into another form of energy. A hydroelectric dam transforms the energy of gravity into electrical energy. An electric oven converts electrical energy into heat. A nuclear power plant converts nuclear energy into heat and heat into electrical energy. The same goes for all forms of energy production or consumption. The total amount of energy in the Universe is constant.

The potential energy of the mass: E = mc²
Even mass is potential energy.

The mass $$m$$ of any body is proportional to the energy $$E$$ that could be released if it were annihilated:

$$m = \frac{E}{c^2}$$

or

$$E = m c^2$$

where $$c$$ is the speed of light.

A mass always has the potential to be annihilated.

The equation $$E =m c^2$$, discovered by Einstein in 1905, can be proven from the fundamental equations of electromagnetism, Maxwell's equations, discovered in 1865. It is explained and proven in the last chapter of this book.

The gradient of a potential
When the work of a force does not depend on the path followed, we say that the force field derives from a potential, because we can calculate the force from the potential by taking its gradient.

To understand the concept of gradient, the simplest way is to think about the relief of a mountain. The height h(x,y) of a point on the mountain surface above a point (x,y) in a plane at sea level is a scalar field. We can call it an altitude field. From this scalar field we can define a vector field. For each point (x,y) we define a vector v(x,y) whose direction is the line of greatest slope of the mountain at this point, which is directed upwards and whose length is the slope of the line of greatest slope (if we rise 10 m when we move horizontally 100 m, the slope is equal to 10% = 10/100 = 0.1). The field of the vectors thus defined is the gradient of the altitude field: v = grad h

In these images a scalar field is represented by shades of gray. Its gradient is represented by the arrows. If the scalar field represents the altitude of a relief, the first represents a cone, the second, an inclined plane.

Level lines are lines of equal altitude. If h were a potential, we would call them equipotential lines.

The lines of greatest slope are the lines that always follow the greatest slope. They are always tangent to the vector field at each point. If h were a potential, we would call them field lines.

The lines of greatest slope are always perpendicular to the level lines. Likewise, the field lines are always perpendicular to the equipotential lines.

The black lines are field lines, and the brown lines are the equipotential lines of the electric field created by two equal and opposite charges.

On a terrain map, adjacent contour lines always indicate the same difference in altitude. They are tighter as the slope is greater. If in the same way we draw adjacent equipotential lines for the same potential difference, the lines are tighter as the field is larger.

For a scalar field $$h$$ in a two-dimensional space, we calculate its gradient by taking its two partial derivatives. grad $$h$$ has components $$\partial h/\partial x$$ and $$\partial h / \partial y$$.

The gradient grad $$V$$ of a scalar field $$V$$ in three-dimensional space is the field of vectors whose components are $$\partial V/\partial x $$, $$\partial V / \partial y$$ and $$\partial V / \partial z$$.

By definition of the potential, if we move a standard body by the distance dx, its potential variation is dV = -fx dx, where fx is the component of the force f in the x direction. So fx = $$- \partial V/\partial x$$. Similarly, fy = $$- \partial V/\partial y$$ and fz = - $$\partial V/\partial z $$.

The force f on a standard body is the opposite of the gradient of the potential $$V$$:

f = -grad $$V$$

This is the general formula that allows us to calculate a force field from a potential.

The Coulomb potential produced by a charge
According to Coulomb's law, the electric field E created by a negative charge -q is the field of vectors directed towards the center of the charge whose magnitude is q/r2 where r is the distance from this center. For a positive charge q, it is the same field, except that the vectors are in opposite directions.

The electric field E created by an electric charge q derives from the coulomb potential V = q/r where r is the distance from the center of the charge:

E = -grad V = -grad q/r

The equipotential surfaces are the spheres centered on the charge. Field lines are all straight lines that extend from the center of the charge.

This potential in a plane which passes through the charge can be represented by an altitude field:

Lines of equal altitude are equipotential lines. They are the intersections of the equipotential spheres with a plane which passes through the electric charge.

-dV/dr = q/r2 = E, the length of the vector E if q is a positive charge.

The Coulomb potential of an electric charge is similar to the gravitational potential of a mass:

The lines are the field lines of the gravitational field produced by the Earth, the gravity field.

The potential produced by several charges
The electric field created by several charges is the sum of the fields created by each of them separately. Now the gradient of a sum is the sum of gradients, because d(f+g)/dx = df/dx + dg/dx. The electric field created by several charges therefore derives from the sum of the electric potentials created by each of them separately. We thus prove that the electric field created by several charges also derives from a potential. Since Newton's potential is mathematically similar to Coulomb's potential, the same is true for the gravitational force.

The field producing two equal and opposite charges can be represented with field lines:

with equipotential lines:

or by representing its potential as a relief:

We can also see the field lines in space:

The gravitational potential produced by the Earth and the Moon is identical to the electric potential produced by two negative electric charges which would have electric charges proportional to the masses of the Earth and the Moon:

The field lines are in blue, the equipotential lines in red.

We can also represent this potential by an altitude field:

The charge of a capacitor
A capacitor is made up of two conductive plates, very close to each other, and separated by an insulating material. Each of the terminals is connected to one of the plates. When the capacitor is turned on, one plate loses some of its electrons and becomes positively charged, while the other plate gains electrons and becomes negatively charged.

We prove with Gauss' theorem (in the chapter on Maxwell's equations) that the electric force field $$\mathbf{E}$$ produced by an infinite charged plane, whose charge density is uniform and equal to $$\sigma$$, is also uniform on each side of the charged plane, perpendicular to it, that its magnitude is E = \frac{\sigma}{2 \epsilon_0}, if it is surrounded by emptiness, and its direction on each side of the plane is opposed to its direction on the other side.

Since the electric field produced by several charges is the sum of the fields produced by each of them, the electric field produced by two parallel charged planes, whose surface charge densities are equal and opposite, is therefore uniform between the planes, perpendicular to them, and its greatness is

$$E = \frac{\sigma}{\epsilon_0}$$

where $$\sigma$$ is the absolute value of the surface charge density,

while it is equal to zero in all the space exterior to the two charged planes.

The field produced by a finite surface capacitor is identical to the previous one except at the edges:

The work of the electric force on a unit charge between the plates is equal to $$Ed$$ where $$d$$ is their distance. This remains true for finished plates far from their edges. The voltage $$V$$ between the plates is therefore proportional to their electric charge $$Q$$. The electric charge is therefore proportional to the voltage:

$$Q = CV$$

where $$C$$ is the capacitance of the capacitor. $$C$$ measures the amount of charge received by one of the plates for a given voltage.

$$C = \frac{\epsilon_0 S}{d} $$

for plates of surface $$S$$ separated by vacuum, separated by a distance $$d$$.

Proof: $$C = Q/V = \frac{\sigma S}{Ed} = \frac{\sigma S}{\sigma d/\epsilon_0} = \frac{\epsilon_0 S}{d}$$

This is why we make capacitors with large surfaces wound on themselves, separated by an insulating film as thin as possible.

$$\epsilon_0$$ is the vacuum permittivity.

If the plates are separated by an insulating material of permittivity $$\epsilon$$, the capacitance of the capacitor is

$$C = \frac{\epsilon S}{d} $$

Electrostatics of conductive materials
A material is conductive when it contains electrical charges that are free to move. In metals, these charges are the conduction electrons. In semiconductors, they can also be holes, absences of electrons that move in a sea of electrons. In ionic solutions like salt water, the mobile electrical charges are positive and negative ions.

Inside a conducting material, the electrostatic field is always zero.

Proof: if the field was not zero, the moving charges would be subject to electric forces which would move them, and the field would not be static.

On the other hand, electric charges can accumulate on the surface of conductive materials. If we place a metallic object near electric charges, its conduction electrons move to exactly compensate for the electric field imposed from the outside to the inside of the metal. The sum of the two fields, the one imposed from the outside and the one imposed by the electrons which have accumulated on the surface, is always equal to zero inside the metal:

On the outer side of the surface of a conductive material, the electric field is perpendicular to the surface.

Proof: if the component of the electric field parallel to the surface was not zero, the surface charges would move to cancel it.

If the surface charge density is positive, the surface electric field is directed outward from the conductive material. If it is negative, it is directed inward.

Proof: if it were the opposite, the electrical forces would push the mobile charges inside the material.

The electric field exerts a force on the surface electric charges but cannot move them, because they cannot move out of the material.

On the surface of a conductive material, the electric field is

$$E = \frac{\sigma}{\epsilon_0}$$

where $$\sigma$$ is the surface charge density.

The proof is given from Gauss' theorem, in the chapter on Maxwell's equations.

Electric charges always move in a direction that tends to cancel out the cause of their movement. Two equal and opposite electric charges produce exactly zero electric field if they are exactly superimposed. When they attract each other, they move in a direction which tends to cancel the electric field which is the cause of their movement.

When the terminals of a capacitor are connected with a metal wire, the conduction electrons are subjected to electrical forces, imposed by the charges on the capacitor plates, which move them in the direction of discharge, not in the direction of an increase in charge.

Electrical polarization
A body is electrically polarized when a charge difference appears between two of its points.

Conductive bodies are polarized when they are placed in a uniform external electric field. Opposite surface electric charges appear on two opposite sides of the object.

Insulating bodies are also polarized by a uniform electric field. Surface electric charges appear on two opposite sides. How is this possible, when by definition, an insulating body has no free electric charges to move?

In an insulating body, the electrons are attached to the nuclei. There is no free conduction electron to pass from one nucleus to another. Around the nucleus to which they are attached, the electrons have retained a little mobility. They can concentrate on one side or the other in order to compensate for the external electrical force to which they are subjected. We can think of electrons trapped in an atom or molecule as an electric fluid which is retained by the nuclei and which can be deformed. This is why insulating bodies can be polarized by an electric field like conducting bodies.

Inside an insulating body, electric charges are displaced uniformly when it is polarized by a uniform external field. The charge density therefore remains zero inside the material. The surface charge density is the only one that varies.

The movement of positive and negative charges inside an insulating body at the moment of its polarization is a transient electric current. But a permanent electric current cannot flow through an insulating material.

When a body is electrically polarized, it orients itself in the direction of the applied electrical forces:

The potential energy of a system of electric charges
How to calculate the electric potential energy of a system of charges?

A charge $$q$$ placed in an electric potential $$V$$ has an electric potential energy $$qV$$.

If we add up the electric potential energies of all the charges with the formula $$E_p = q V$$, we do not find the right result. Why ?

To calculate the potential energy of a system, we must calculate the energy spent or received when it is assembled. When we assemble electric charges, the electric field they must pass through is not the same at the beginning and at the end of the assembly. The potential $$V$$ that we calculate when the system is assembled is not the potential of the field that the charges encountered when they were assembled, it is only the potential of the field that a new charge would encounter if brought near the system.

The first of the assembled charges does not encounter any electric force field to be put into place, because no charge is present before it. The second charge meets the field produced by the first. The third charge meets the field produced by the first two, and so on until the last charge, which encounters the field produced by all the previous ones.

Example: the potential energy of a charged capacitor

To charge a capacitor, electrons must be moved from one of its plates to the other. The first charge $$dq$$ moved encounters no field, because the capacitor is not charged. The work $$dW$$ that must be done to move it is therefore $$dW=0$$. If the capacitor is already charged by a charge $$q = \int dq$$, a new charge $$dq$$ encounters an electric force field, therefore a potential difference between its starting point and its arrival point $$V_2 - V_1 = \frac{q}{C}$$. So

$$dW = (V_2 - V_1) dq = \frac{q}{C}dq$$

$$W = \int dW = \int \frac{q}{C}dq = \frac{1}{2} CV^2$$

$$E_p = \frac{1}{2} CV^2$$ is therefore the electric potential energy of a capacitor charged by a charge $$Q = CV$$, where $$C$$ is its capacitance and $$V$$ the potential difference between its plates.

Where is the electric potential energy?
Electric potential energy is attributed to electric charges. Is this energy carried by the charges? Is it located on the charges?

$$E = mc^2$$. Mass is always energy. Energy always has mass. This equation is proven at the end of this book, where it is shown that light trapped in a box increases the mass of the box. Light therefore has a mass equal to its energy divided by $$c^2$$.

If the electric potential energy were localized on the charges, variations in their energy would cause their mass to vary. But this effect has never been observed.

The electric potential energy of a system of charges is in all the space where they produce an electric field, it is carried by the electric field. The volume density of electrical energy in an electrostatic field $$\mathbf{E}$$ is

$$\frac{dE_p}{dV} = \frac{1}{2} \epsilon_0 \mathbf{E}^2$$

where $$dE_p$$ is the electric potential energy contained in a small volume $$dV$$.

When we bring two electric charges of the same sign together, we increase the energy of the electric field:

If we bring two charges of opposite signs together, we reduce the energy of the electric field. The same is true for the nuclear forces that hold neutrons and protons together in a nucleus. We have to provide them with energy to separate them. This is why their mass is greater when they are separated than when they are united:

It takes infinite energy to separate the three quarks that make a proton, or a neutron. This is why we can never observe an isolated quark.

Let us show that $$\frac{dE_p}{dV} = \frac{1}{2} \epsilon_0 \mathbf{E}^2$$ allows us to correctly calculate the electric potential energy of a charged capacitor:

$$E_p = \int_V dE_p = \int_V \epsilon_0 \mathbf{E}^2 dV = \frac{Sd \sigma^2}{2 \epsilon_0} $$

where $$S$$ is the surface area of the capacitor, $$d$$ the distance between the plates, $$Sd$$ the volume between the plates and $$\frac{\sigma }{\epsilon_0}$$ the field $$E$$ produced by a surface charge density $$\sigma$$.

Now

$$C = \frac{\epsilon_0 S}{d}$$ and $$V = Ed = \frac{\sigma d}{\epsilon_0}$$

so

$$E_p = \frac{1}{2} C V^2$$

When we define the potential, we are free to choose a point of zero potential. To calculate electric forces, any choice is suitable because two potentials that differ by a constant have the same gradient. But to calculate the energy and the presence of its mass, we are obviously not free to modify the energy of all the charges by choosing another point of zero potential. The point of zero potential must be chosen in such a way that an electric charge can be placed there without making any effort. This is why when we calculate the electrostatic energy of a system of charges, we assume that they are placed in empty space, and we define a zero potential at infinity. The force exerted by electric charges tends to zero at infinity. There is no effort to be made against their electric force if we are very far from them.

When a dipole moment is created by the separation of equal and opposite charges, as when charging a capacitor, we can reason as if the charge density were initially zero everywhere. So there is no electric force anywhere. Any point can therefore be chosen as a point of zero potential.


text:
User talk:182.180.12.146

February 2024
MathXplore (discuss • contribs) 12:44, 29 February 2024 (UTC)

title: User talk:182.180.12.146


text:
Moving objects in retarded gravitational potentials of an expanding spherical shell

Contents

 * 1) /Preface/
 * 2) /Brief historical review/
 * 3) /Classical approach/
 * 4) /Retarded gravitational potentials/
 * 5) /Gravitational redshift/
 * 6) /Conclusion/

Appendix

 * 1) /Table with computed results/
 * 2) /Java program/

Summary of the project

 * Target audience: Astronomers, astrophysicists, physicists, mathematicians
 * Learning objectives: Application of retarded gravitational potentials and gravitational redshift on very large scales.
 * Contact person: User:Bautsch
 * Are co-authors currently desired? Yes. Corrections of obvious errors directly in the text; content please after discussion.
 * Guidelines for co-authors: Wikimedia-like.


text:
Flora of New York/gbif

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title: Flora of New York/gbif


text: User talk:Abdela yesuf

title: User talk:Abdela yesuf