text:
# Unity Dangling pointers in containers (undefined behavior)

This topic is 3990 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

This is just a nit-picky post, mostly to Zahlman and MaulingMonkey. I have rated both of you up in the past as I have always found you two to be very helpful, so don't take offense to the post, I'm merely trying to get to the bottom of this. I would have replied to the original thread that started this discussion but I was away on business and it was closed by the time I got back. I recently saw a new post on c.l.c++.m that again discusses the fact that leaving a dangling pointer in a std container is undefined behavior (I say "again discussing" because, like I brought up in the original thread, this comes up rather often there, always with the same result - "it is undefined behavior"). Now in practice I almost always use smart pointers within my containers, so I never have to worry about this, and when there are raw pointers, yes, I use the function object and std::for_each idiom. In reply to MaulingMonkey's last post, where he stated "given that dangling pointers within containers are legal and well defined behavior so long as they are not dereferenced", I believe the issue is that the standard says the only legal thing you can do with a dangling pointer is assign it a new (valid) value. Any other "use" of the pointer is undefned, and even an rvalue to lvalue conversion is considered use, it does not have to be dereferenced, merely used. Thoughts? [Edited by - mfawcett on March 19, 2007 9:37:44 AM]

##### Share on other sites
After reading that last thread, I was under the impression that this "dangling pointers in containers result in undefined behavior" was possibly a misunderstanding of the standard. The standard talks about uninitialized pointers having a "singular value" or something like that. Unless you're putting uninitialized pointers in your container, the result isn't going to be undefined. You end up with a well defined dangling pointer. As far as I know, copying a dangling pointer is a well defined operation.

The issue is this: Is copying an invalid pointer an undefined operation? The standard (according to a post in the other thread) says that use of an invalid pointer is undefined, but I don't believe that copying the value of the pointer counts as use of that pointer. An invalid pointer is not necessarily a "singular value" (undefined value).

##### Share on other sites
Well, the singular value thing was my fault. I posted an irrelevant section of the standard. The second quote was the correct one, I believe.

3.7.3.2 paragraph 4
"...The effect of using an invalid pointer value (including passing it to a deallocation function) is undefined.33)"

"Using" does not only mean dereferencing in my understanding. It means any use other than:

my_dangling_ptr = 0;// ormy_dangling_ptr = valid_ptr;

which, as far as I can tell, is the only legal thing you can do with a dangling pointer.

##### Share on other sites
I'm not going to quote standards, as I don't have access to a copy, but I cannot see the point you are making in that thread.

Even the pendant in me cannot see the point you are making. [smile] The deletion of each pointer in the container would only result in undefined behaviour were it not cleared afterwards.

Whatever about a small thinking point at the end of that other thread, but to devote an entire thread to this "topic"...

I think I could sleep at night were I to use the delete-the-pointers-then-clear method. [grin]

##### Share on other sites
Quote:
 Original post by rip-offWhatever about a small thinking point at the end of that other thread, but to devote an entire thread to this "topic"...I think I could sleep at night were I to use the delete-the-pointers-then-clear method. [grin]

##### Share on other sites
I'd much rather completely waste my time on something else than revisit this.

Or do something useful like working on my replacement for the FUBAR that is C++.

Presuming for a second that it is undefined behavior, I'm going to propose that each of the following is more likely to be a problem:

1) The workaround to avoid the behavior accidentally invoking significant undefined behavior
2) Death due to bus collision related injuries
3) Death due to llama related injuries
4) Death due to a world war caused by significant undefined behavior

In conclusion, the issue at stake would be a defect in the standard rather than that of any code IMO. Regardless, this has since fallen out of my Cone of Caring.

##### Share on other sites
This is actually a problem throughout the standard, it has a tendency to be relatively vuage about certain points that leads to questionably defined behavior (and questionably undefined behavior). One thing we can note though is how it deals with pointers that are explicitly outside of the range of valid values for an object: that is, given an object o, and a pointer p such that p = &o, then p+1 points one past o and is a valid pointer, but p+2 is not only an invalid pointer, but results in undefined behavior. Applying this same context to a dangling pointer, one could show that doing anything with the dangling pointer (with the exception of reassignment) is also undefined behavior, since it points outside of the range of legal values.

In reality, C++0x should hopefully clear this up somewhat, but I haven't actually seen any efforts to do such (mostly just library work with a little language work to get the libraries working).

##### Share on other sites
I agree with you MaulingMonkey, which is why I tried to caveat every post with "in practice it's not an issue", or "in my own code I don't even worry about this" type phrases. Your tone is less than pleasant, however.

Thank you, Washu, for a very nice reply.

##### Share on other sites
Quote:
 Original post by mfawcettWell, the singular value thing was my fault. I posted an irrelevant section of the standard. The second quote was the correct one, I believe.3.7.3.2 paragraph 4"...The effect of using an invalid pointer value (including passing it to a deallocation function) is undefined.33)""Using" does not only mean dereferencing in my understanding. It means any use other than:my_dangling_ptr = 0;// ormy_dangling_ptr = valid_ptr;which, as far as I can tell, is the only legal thing you can do with a dangling pointer.

So your argument against dangling pointers in SC++L containers is (correct me if I'm wrong) that the containers are allowed to copy contained values at any time and that copying an invalid pointer value is undefined behaviour:
int * i = new int;delete i;int * j = i; // undefined behaviour.

Now riddle me this. If copying an invalid pointer value is undefined behaviour then why does the quoted section of the standard explicitly highlight that passing an invalid pointer value to a deallocation function is undefined? All of the standard deallocation functions take their parameters by value, so if copying an invalid pointer value was undefined behaviour then passing an invalid pointer value to a deallocation function would implicitly by undefined behaviour due to the pass-by-value. Furthermore, passing an invalid pointer value to any function that tooks its parameter by value would be undefined behaviour. So why did the standards committee feel it necessary to explicitly state "including passing it to a deallocation function"?

Nowhere does the C++ standard define "use", in the context of the above quote from the standard. Neither can I find any reasonable argument, based on any conceivable machine architecture, for copying an invalid pointer value to be undefined behaviour. Significant parts of the C++ standard are based on possible underlying architectures. The argument for pointers outside the [array, array + size] range being undefined can be seen in architectures with segment/offset based pointers and in pointer under/overflow. The argument about pointers with singular values is harder to see, but one can envisage an architecture where pointers are specially handled on the hardware level and as such have certain constraints which may be violated by copying an uninitialised pointer. I can see no reasonable argument for copying a pointer value which was known to be valid at a previous point in time to be undefined behaviour, nor can I find any clear justification in the standard for it to be.

I'm quite prepared to be proven wrong, but I'm afraid I'm going to require you to be far more persuasive than you have been so far.

Σnigma

##### Share on other sites
Quote:
 Original post by EnigmaNeither can I find any reasonable argument, based on any conceivable machine architecture, for copying an invalid pointer value to be undefined behaviour.

Nor I, and I doubt anyone could. This wasn't a discussion about it being sensible or not, merely whether it was so.

Quote:
 Original post by EnigmaI'm quite prepared to be proven wrong, but I'm afraid I'm going to require you to be far more persuasive than you have been so far.

I'm not enough of an expert to persuade you. My evidence would simply be to point you at the newsgroups to view what the experts there have said, but there seems to be a bit of contention there too, with a few parties arguing that it's not UB.

For instance, here is a quote from James Kanze:

"Formally, I think that even those have undefined behavior. You
have to remove the pointer from the container in some way
(removing the element or changing its value) *before* the
delete. The simple presence of the pointer in the container
after delete is undefined behavior..."

and Seungbeom Kim:

"Except when the pointer is in a container, in which case you have to
explicitly set the pointer to null to avoid undefined behaviour..."

Do you see any harm in simply defining a delete_ptr struct as so?
struct delete_ptr{   template <typename T>   void operator()(const T *&ptr) const   {      delete ptr;      ptr = 0;   }};std::for_each(vec.begin(), vec.end(), delete_ptr());

Regardless, I really tried to preface all my posts saying that "in practice this is not an issue", so I'm not sure where all of the aggressiveness is coming from.

Signed,

Merely Interested In The Standard, Not Interested In A Fight.

##### Share on other sites
Quote:
 Original post by mfawcettI agree with you MaulingMonkey, which is why I tried to caveat every post with "in practice it's not an issue", or "in my own code I don't even worry about this" type phrases. Your tone is less than pleasant, however.

If you've expected pleasantries from me, it's clear you've confused me with some other monkey. Monkey Jesus, prehaps. Or Monkey Budah.

There's a reason my nick isn't MassagingMonkey.

That said, given that I've linked one of my favorite webcomics for relevant humor, sharing this possibly previously unknown (to you) gem of humor (as it is in my opinion), I'm left wondering why my above-par jollyness is interpreted as sub-par compared to the expected.

I replied to this post as a result of being named in the original post. I felt a post detailing why I would not continue the discussion to be relevant, and so it was supplied. Do with it what you will. I've already stated what I'll do.

##### Share on other sites
I'm not sure whether the Standard can specify any stronger guarantees regarding singular/dangling pointers without needlessly limiting the range of potential hardware on which a C++ program can be run.

For instance, I can certainly imagine a security-enhanced CPU where the mere act of loading an invalid(* pointer to a register triggers a hardware trap or an interrupt, specifically to catch unitialized pointers before doing something much worse, such as using them as jump addresses.

*) an invalid bit pattern, or a value outside of the memory allocated for the process.

##### Share on other sites
Quote:
 Original post by SharlinI'm not sure whether the Standard can specify any stronger guarantees regarding singular/dangling pointers without needlessly limiting the range of potential hardware on which a C++ program can be run.For instance, I can certainly imagine a security-enhanced CPU where the mere act of loading an invalid(* pointer to a register triggers a hardware trap or an interrupt, specifically to catch unitialized pointers before doing something much worse, such as using them as jump addresses.*) an invalid bit pattern, or a value outside of the memory allocated for the process.

As far as I see, such register would have to be dedicated to memory addresses only and thus needed to be used only when accessing memory indirectly through it. A compiler backend could store the pointer in a general purpose register until the pointer would actually be dereferenced.

##### Share on other sites
Look up the section on reinterprete_cast<>() in the standard im pretty sure it uses the same wording, however i dont have a copy to check, and its a similar context hence since im pretty sure its valid to copy the result of reinterprete_cast id say copying a dangling pointer is valid.

Of course if im wrong about what the standard says on reinterprete_cast<>() then just ignore me :)

##### Share on other sites
Quote:
 Original post by Julian90Look up the section on reinterprete_cast<>() in the standard im pretty sure it uses the same wording, however i dont have a copy to check, and its a similar context hence since im pretty sure its valid to copy the result of reinterprete_cast id say copying a dangling pointer is valid.Of course if im wrong about what the standard says on reinterprete_cast<>() then just ignore me :)

I looked up the section. From what I can tell, the result of reinterpret_cast can either be specified, unspecified, implementation defined, or result in UB. It says nothing about what happens when you copy those values, just that the cast will result in one of the 4 behaviors.

##### Share on other sites
Quote:
 Original post by MaulingMonkeyThat said, given that I've linked one of my favorite webcomics for relevant humor, sharing this possibly previously unknown (to you) gem of humor (as it is in my opinion), I'm left wondering why my above-par jollyness is interpreted as sub-par compared to the expected.I replied to this post as a result of being named in the original post. I felt a post detailing why I would not continue the discussion to be relevant, and so it was supplied. Do with it what you will. I've already stated what I'll do.

Apologies, I must have read into something from your post that wasn't there. That's the Internet for you...

##### Share on other sites
Quote:
 Original post by EnigmaSo your argument against dangling pointers in SC++L containers is (correct me if I'm wrong) that the containers are allowed to copy contained values at any time and that copying an invalid pointer value is undefined behaviour:int * i = new int;delete i;int * j = i; // undefined behaviour.

Yes, apparently even the C standard says so.

*Any* use other than assignment is UB. That means that an invalid pointer is not copyable.

Apparently there have also been architectures that existed(still exist?) where copying an invalid pointer did lead to a hardware trap. (I did not know about this until recently).

Quote:
 Original post by EnigmaI'm quite prepared to be proven wrong, but I'm afraid I'm going to require you to be far more persuasive than you have been so far.

STD Containers require their elements be Copyable and Assignable. They do not specify time constraints as to when that might be, so that means the elements must be Copyable and Assignable always (when in the container). The moment you delete a pointer that still exists in a container, you have UB, regardless if immediately after you do a clear().

The temporary in my code was for that specific reason.
T *ptr = vec.back();vec.pop_back();delete ptr;

It *did* serve a purpose.

##### Share on other sites
I agree with you that SC++L containers require CopyConstructible and Assignable elements. I disagree that the C++ Standard states that a deleted pointer value is not CopyConstructible or Assignable. The thread you linked to quotes from the C99 standard. In C99 it seems quite clear that copying a deleted pointer value is undefined behaviour. In C89 it could be argued that copying a deleted pointer value is undefined behaviour (based on the draft copy I read). The C++ Standard, which was based on the C89 standard contains nothing that I can find to suggest that copying a deleted pointer value is undefined behaviour. This may be a defect in the C++ Standard, but I have yet to see a convincing argument for copying a pointer with indeterminate value to be undefined behaviour in C++.

In fact just looking again the C++ standard even contains an example when an object (not a pointer) with indeterminate value is copied, and no reference is made to this being undefined behaviour:
Quote:
 C++ Standard, Section 3.3.1, Paragraph 1The point of declaration for a name is immediately after its complete declarator (clause 8) and before its initializer (if any), except as noted below. [Example:   int x = 12;   { int x = x; }Here the second x is initialized with its own (indeterminate) value. ]

Σnigma

##### Share on other sites
4.1p1 (Lvalue to rvalue conversions): "If the object to which the lvalue refers ... is uninitialized, a program that necessitates this conversion has undefined behavior."

That's only in reference to your latest post. I don't think it has bearing on invalid pointers, but I could be mistaken.

• 10
• 15
• 11
• 10
• 12
• ### Similar Content

• Good day,

I just wanted to share our casual game that is available for android.

Description: Fight your way from the ravenous plant monster for survival through flips. The rules are simple, drag and release your phone screen. Improve your skills and show it to your friends with the games quirky ranks. Select an array of characters using the orb you acquire throughout the game.

Trailer:

• Hello fellow devs!
Once again I started working on an 2D adventure game and right now I'm doing the character-movement/animation. I'm not a big math guy and I was happy about my solution, but soon I realized that it's flawed.
My player has 5 walking-animations, mirrored for the left side: up, upright, right, downright, down. With the atan2 function I get the angle between player and destination. To get an index from 0 to 4, I divide PI by 5 and see how many times it goes into the player-destination angle.

In Pseudo-Code:
angle = atan2(destination.x - player.x, destination.y - player.y) //swapped y and x to get mirrored angle around the y axis
index = (int) (angle / (PI / 5));
PlayAnimation(index); //0 = up, 1 = up_right, 2 = right, 3 = down_right, 4 = down

Besides the fact that when angle is equal to PI it produces an index of 5, this works like a charm. Or at least I thought so at first. When I tested it, I realized that the up and down animation is playing more often than the others, which is pretty logical, since they have double the angle.

What I'm trying to achieve is something like this, but with equal angles, so that up and down has the same range as all other directions.

I can't get my head around it. Any suggestions? Is the whole approach doomed?

Thank you in advance for any input!

• By khawk
Watch the latest from Unity.

• By GytisDev
Hello,
without going into any details I am looking for any articles or blogs or advice about city building and RTS games in general. I tried to search for these on my own, but would like to see your input also. I want to make a very simple version of a game like Banished or Kingdoms and Castles,  where I would be able to place like two types of buildings, make farms and cut trees for resources while controlling a single worker. I have some problem understanding how these games works in the back-end: how various data can be stored about the map and objects, how grids works, implementing work system (like a little cube (human) walks to a tree and cuts it) and so on. I am also pretty confident in my programming capabilities for such a game. Sorry if I make any mistakes, English is not my native language.
• By Ovicior
Hey,
So I'm currently working on a rogue-like top-down game that features melee combat. Getting basic weapon stats like power, weight, and range is not a problem. I am, however, having a problem with coming up with a flexible and dynamic system to allow me to quickly create unique effects for the weapons. I want to essentially create a sort of API that is called when appropriate and gives whatever information is necessary (For example, I could opt to use methods called OnPlayerHit() or IfPlayerBleeding() to implement behavior for each weapon). The issue is, I've never actually made a system as flexible as this.
My current idea is to make a base abstract weapon class, and then have calls to all the methods when appropriate in there (OnPlayerHit() would be called whenever the player's health is subtracted from, for example). This would involve creating a sub-class for every weapon type and overriding each method to make sure the behavior works appropriately. This does not feel very efficient or clean at all. I was thinking of using interfaces to allow for the implementation of whatever "event" is needed (such as having an interface for OnPlayerAttack(), which would force the creation of a method that is called whenever the player attacks something).

Here's a couple unique weapon ideas I have:
Explosion sword: Create explosion in attack direction.
Cold sword: Chance to freeze enemies when they are hit.
Electric sword: On attack, electricity chains damage to nearby enemies.

I'm basically trying to create a sort of API that'll allow me to easily inherit from a base weapon class and add additional behaviors somehow. One thing to know is that I'm on Unity, and swapping the weapon object's weapon component whenever the weapon changes is not at all a good idea. I need some way to contain all this varying data in one Unity component that can contain a Weapon field to hold all this data. Any ideas?

I'm currently considering having a WeaponController class that can contain a Weapon class, which calls all the methods I use to create unique effects in the weapon (Such as OnPlayerAttack()) when appropriate.


text:
# Hidden Roots Part 2

Calculus Level 5

$$\mathfrak{F}(x)=\dfrac{1}{x-1}+\dfrac{1}{x-2}+\dfrac{1}{x-3} + \ldots +\dfrac{1}{x-99}+\dfrac{1}{x-100}$$

Given the above function $$\mathfrak{F}(x)$$ and

$$\large x_{1},x_{2}, \ldots ,x_{n}$$ are its roots in some order.

Find the maximum possible value of value
$\large\dfrac{ [x_{1} ]-[ x_{2} ]+ [ x_{3} ]-[ x_{4} ]+ \ldots \pm[ x_{n} ]} {n+1}$

Details and Assumptions

$$[m]$$ represents greatest integer function of $$m$$

×

format: plain


text:
## Abstract and Applied Analysis

### The Study of Triple Integral Equations with Generalized Legendre Functions

#### Abstract

A method is developed for solutions of two sets of triple integral equations involving associated Legendre functions of imaginary arguments. The solution of each set of triple integral equations involving associated Legendre functions is reduced to a Fredholm integral equation of the second kind which can be solved numerically.

#### Article information

Source
Abstr. Appl. Anal., Volume 2008 (2008), Article ID 395257, 12 pages.

Dates
First available in Project Euclid: 10 February 2009

https://projecteuclid.org/euclid.aaa/1234298996

Digital Object Identifier
doi:10.1155/2008/395257

Mathematical Reviews number (MathSciNet)
MR2453145

Zentralblatt MATH identifier
1160.45301

#### Citation

Singh, B. M.; Rokne, J.; Dhaliwal, R. S. The Study of Triple Integral Equations with Generalized Legendre Functions. Abstr. Appl. Anal. 2008 (2008), Article ID 395257, 12 pages. doi:10.1155/2008/395257. https://projecteuclid.org/euclid.aaa/1234298996

#### References

• A. A. Babloian, Solutions of certain dual integral equations,'' Prikladnaya Matematika i Mekhanika, vol. 28, no. 6, pp. 1015--1023, 1964, English translation in Journal of Applied Mathematics and Mechanics, vol. 28, no. 6, pp. 1227--1236, 1964.
• R. S. Pathak, On a class of dual integral equations,'' Koninklijke Nederlandse Akademie van Wetenschappen, vol. 40, no. 4, pp. 491--501, 1978.
• B. N. Mandal, A note on dual integral equations involving associated Legendre function,'' International Journal of Mathematics and Mathematical Sciences, vol. 15, no. 3, pp. 601--604, 1992.
• B. M. Singh, J. Rokne, and R. S. Dhaliwal, The study of dual integral equations with generalized Legendre functions,'' Journal of Mathematical Analysis and Applications, vol. 304, no. 2, pp. 725--733, 2005.
• K. N. Srivastava, On some triple integral equations involving Legendre functions of imaginary argument,'' Journal of Maulana Azad College of Technology, vol. 1, pp. 54--67, 1968.
• J. C. Cooke, Triple integral equations,'' The Quarterly Journal of Mechanics and Applied Mathematics, vol. 16, no. 2, pp. 193--203, 1963.
• J. C. Cooke, Some further triple integral equation solutions,'' Proceedings of the Edinburgh Mathematical Society, vol. 13, pp. 303--316, 1963.
• J. C. Cooke, The solution of triple integral equations in operational form,'' The Quarterly Journal of Mechanics and Applied Mathematics, vol. 18, no. 1, pp. 57--72, 1965.
• J. C. Cooke, The solution of triple and quadruple integral equations and Fourier-Bessel series,'' The Quarterly Journal of Mechanics and Applied Mathematics, vol. 25, no. 2, pp. 247--263, 1972.
• C. J. Tranter, Some triple integral equations,'' Proceedings of the Glasgow Mathematical Association, vol. 4, pp. 200--203, 1960.
• E. R. Love and D. L. Clements, A transformation of Cooke's treatment of some triple integral equations,'' Journal of the Australian Mathematical Society. Series B, vol. 19, no. 3, pp. 259--288, 1976.
• N. Srivastava, On triple integral equations involving Bessel function as kernel,'' Journal of Maulana Azad College of Technology, vol. 21, pp. 39--50, 1988.
• I. N. Sneddon, Mixed Boundary Value Problems in Potential Theory, North-Holland, Amsterdam, The Netherlands, 1966.
• A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Tables of Integral Transforms. Vol. II, McGraw Hill, New York, NY, USA, 1954.
• A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Tables of Integral Transforms. Vol. I, McGraw Hill, New York, NY, USA, 1954.
• W. Magnus, F. Oberhettinger, and R. P. Soni, Formulas and Theorems for the Special Functions of Mathematical Physics, Die Grundlehren der Mathematischen Wissenschaften. 52, Springer, New York, NY, USA, 1966. \endthebibliography


text:
## How to Add References in Footnotes in SciFlow

SciFlow is an exciting platform for collaborative academic writing. Perhaps similar to Authorea, SciFlow comes with no restrictions. One limitation I faced was that it seemed impossible to add reference in footnotes. If you enter a footnote, and add a reference there, the reference is added after the footnote. That’s not what we want. Let’s walk through the workaround:

You can add references in footnotes, though, if you copy the text (with the reference) into a footnote. To do so, write the text of the footnote on a new line, select the entire paragraph, and click on the “footnote” symbol (or cut and paste).

It turns out, there is a bug in the way references in footnotes are displayed (which the developers expect to iron out very soon), which made me believe that you cannot add references in footnotes. You get a “NO RENDERER SUPPLIED” error instead of the reference field.


text:
# Electricity

Last updated

Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. In early days, electricity was considered as being not related to magnetism. Later on, many experimental results and the development of Maxwell's equations indicated that both electricity and magnetism are from a single phenomenon: electromagnetism. Various common phenomena are related to electricity, including lightning, static electricity, electric heating, electric discharges and many others.

Physics is the natural science that studies matter and its motion and behavior through space and time and that studies the related entities of energy and force. Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves.

A phenomenon is any thing which manifests itself. Phenomena are often, but not always, understood as "things that appear" or "experiences" for a sentient being, or in principle may be so.

Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. There are two types of electric charges; positive and negative. Like charges repel and unlike attract. An object with an absence of net charge is referred to as neutral. Early knowledge of how charged substances interact is now called classical electrodynamics, and is still accurate for problems that do not require consideration of quantum effects.

## Contents

The presence of an electric charge, which can be either positive or negative, produces an electric field. The movement of electric charges is an electric current and produces a magnetic field.

An electric field is a vector field surrounding an electric charge that exerts force on other charges, attracting or repelling them. Mathematically the electric field is a vector field that associates to each point in space the force, called the Coulomb force, that would be experienced per unit of charge by an infinitesimal test charge at that point. The units of the electric field in the SI system are newtons per coulomb (N/C), or volts per meter (V/m). Electric fields are created by electric charges, or by time-varying magnetic fields. Electric fields are important in many areas of physics, and are exploited practically in electrical technology. On an atomic scale, the electric field is responsible for the attractive force between the atomic nucleus and electrons that holds atoms together, and the forces between atoms that cause chemical bonding. Electric fields and magnetic fields are both manifestations of the electromagnetic force, one of the four fundamental forces of nature.

An electric current is a flow of electric charge. In electric circuits this charge is often carried by electrons moving through a wire. It can also be carried by ions in an electrolyte, or by both ions and electrons such as in an ionized gas (plasma).

A magnetic field is a vector field that describes the magnetic influence of electrical currents and magnetized materials. In everyday life, the effects of magnetic fields are often seen in permanent magnets, which pull on magnetic materials and attract or repel other magnets. Magnetic fields surround and are created by magnetized material and by moving electric charges such as those used in electromagnets. Magnetic fields exert forces on nearby moving electrical charges and torques on nearby magnets. In addition, a magnetic field that varies with location exerts a force on magnetic materials. Both the strength and direction of a magnetic field varies with location. As such, it is an example of a vector field.

When a charge is placed in a location with a non-zero electric field, a force will act on it. The magnitude of this force is given by Coulomb's law. Thus, if that charge were to move, the electric field would be doing work on the electric charge. Thus we can speak of electric potential at a certain point in space, which is equal to the work done by an external agent in carrying a unit of positive charge from an arbitrarily chosen reference point to that point without any acceleration and is typically measured in volts.

Coulomb's law, or Coulomb's inverse-square law, is a law of physics for quantifying Coulomb's force, or electrostatic force. Electrostatic force is the amount of force with which stationary, electrically charged particles either repel, or attract each other. This force and the law for quantifying it, represent one of the most basic forms of force used in the physical sciences, and were an essential basis to the study and development of the theory and field of classical electromagnetism. The law was first published in 1785 by French physicist Charles-Augustin de Coulomb.

In physics, a force is said to do work if, when acting, there is a displacement of the point of application in the direction of the force. For example, when a ball is held above the ground and then dropped, the work done on the ball as it falls is equal to the weight of the ball multiplied by the distance to the ground. When the force is constant and the angle between the force and the displacement is θ, then the work done is given by W = Fs cos θ.

An electric potential is the amount of work needed to move a unit of positive charge from a reference point to a specific point inside the field without producing an acceleration. Typically, the reference point is the Earth or a point at infinity, although any point beyond the influence of the electric field charge can be used.

Electricity is at the heart of many modern technologies, being used for:

Electric power is the rate, per unit time, at which electrical energy is transferred by an electric circuit. The SI unit of power is the watt, one joule per second.

Electronics comprises the physics, engineering, technology and applications that deal with the emission, flow and control of electrons in vacuum and matter. The identification of the electron in 1897, along with the invention of the vacuum tube, which could amplify and rectify small electrical signals, inaugurated the field of electronics and the electron age.

Passivity is a property of engineering systems, used in a variety of engineering disciplines, but most commonly found in analog electronics and control systems. A passive component, depending on field, may be either a component that consumes but does not produce energy or a component that is incapable of power gain.

Electrical phenomena have been studied since antiquity, though progress in theoretical understanding remained slow until the seventeenth and eighteenth centuries. Even then, practical applications for electricity were few, and it would not be until the late nineteenth century that electrical engineers were able to put it to industrial and residential use. The rapid expansion in electrical technology at this time transformed industry and society, becoming a driving force for the Second Industrial Revolution. Electricity's extraordinary versatility means it can be put to an almost limitless set of applications which include transport, heating, lighting, communications, and computation. Electrical power is now the backbone of modern industrial society. [1]

Electrical engineering is a professional engineering discipline that generally deals with the study and application of electricity, electronics, and electromagnetism. This field first became an identifiable occupation in the later half of the 19th century after commercialization of the electric telegraph, the telephone, and electric power distribution and use. Subsequently, broadcasting and recording media made electronics part of daily life. The invention of the transistor, and later the integrated circuit, brought down the cost of electronics to the point they can be used in almost any household object.

The Second Industrial Revolution, also known as the Technological Revolution, was a phase of rapid industrialization in the final third of the 19th century and the beginning of the 20th. The First Industrial Revolution, which ended in the early to mid 1800s, was punctuated by a slowdown in macroinventions before the Second Industrial Revolution in 1870. Though a number of its characteristic events can be traced to earlier innovations in manufacturing, such as the establishment of a machine tool industry, the development of methods for manufacturing interchangeable parts and the invention of the Bessemer Process to produce steel, the Second Industrial Revolution is generally dated between 1870 and 1914.

In thermodynamics, motive power is a natural agent, such as water or steam, wind or electricity, used to impart motion to machinery such as an engine. Motive power may also be a locomotive or a motor, which provides motive power to a system. Motive power may be thought of as a synonym for either "work", i.e. force times distance [J], or "power" [J/s].

## History

Long before any knowledge of electricity existed, people were aware of shocks from electric fish. Ancient Egyptian texts dating from 2750 BCE referred to these fish as the "Thunderer of the Nile", and described them as the "protectors" of all other fish. Electric fish were again reported millennia later by ancient Greek, Roman and Arabic naturalists and physicians. [2] Several ancient writers, such as Pliny the Elder and Scribonius Largus, attested to the numbing effect of electric shocks delivered by catfish and electric rays, and knew that such shocks could travel along conducting objects. [3] Patients suffering from ailments such as gout or headache were directed to touch electric fish in the hope that the powerful jolt might cure them. [4] Possibly the earliest and nearest approach to the discovery of the identity of lightning, and electricity from any other source, is to be attributed to the Arabs, who before the 15th century had the Arabic word for lightning ra‘ad (رعد) applied to the electric ray. [5]

An electric fish is any fish that can generate electric fields. A fish that can generate electric fields is said to be electrogenic while a fish that has the ability to detect electric fields is said to be electroreceptive. Most electrogenic fish are also electroreceptive. Electric fish species can be found both in the ocean and in freshwater rivers of South America (Gymnotiformes) and Africa (Mormyridae). Many fish such as sharks, rays and catfishes can detect electric fields and are thus electroreceptive, but they are not classified as electric fish because they cannot generate electricity. Most common bony fish (teleosts), including most fish kept in aquaria or caught for food, are neither electrogenic nor electroreceptive.

Ancient Egypt was a civilization of ancient North Africa, concentrated along the lower reaches of the Nile River in the place that is now the country Egypt. Ancient Egyptian civilization followed prehistoric Egypt and coalesced around 3100 BC with the political unification of Upper and Lower Egypt under Menes. The history of ancient Egypt occurred as a series of stable kingdoms, separated by periods of relative instability known as Intermediate Periods: the Old Kingdom of the Early Bronze Age, the Middle Kingdom of the Middle Bronze Age and the New Kingdom of the Late Bronze Age.

The 28th century BC was a century which lasted from the year 2800 BC to 2701 BC.

Ancient cultures around the Mediterranean knew that certain objects, such as rods of amber, could be rubbed with cat's fur to attract light objects like feathers. Thales of Miletus made a series of observations on static electricity around 600 BCE, from which he believed that friction rendered amber magnetic, in contrast to minerals such as magnetite, which needed no rubbing. [6] [7] [8] [9] Thales was incorrect in believing the attraction was due to a magnetic effect, but later science would prove a link between magnetism and electricity. According to a controversial theory, the Parthians may have had knowledge of electroplating, based on the 1936 discovery of the Baghdad Battery, which resembles a galvanic cell, though it is uncertain whether the artifact was electrical in nature. [10]

Electricity would remain little more than an intellectual curiosity for millennia until 1600, when the English scientist William Gilbert wrote De Magnete , in which he made a careful study of electricity and magnetism, distinguishing the lodestone effect from static electricity produced by rubbing amber. [6] He coined the New Latin word electricus ("of amber" or "like amber", from ἤλεκτρον, elektron, the Greek word for "amber") to refer to the property of attracting small objects after being rubbed. [11] This association gave rise to the English words "electric" and "electricity", which made their first appearance in print in Thomas Browne's Pseudodoxia Epidemica of 1646. [12]

Further work was conducted in the 17th and early 18th centuries by Otto von Guericke, Robert Boyle, Stephen Gray and C. F. du Fay. [13] Later in the 18th century, Benjamin Franklin conducted extensive research in electricity, selling his possessions to fund his work. In June 1752 he is reputed to have attached a metal key to the bottom of a dampened kite string and flown the kite in a storm-threatened sky. [14] A succession of sparks jumping from the key to the back of his hand showed that lightning was indeed electrical in nature. [15] He also explained the apparently paradoxical behavior [16] of the Leyden jar as a device for storing large amounts of electrical charge in terms of electricity consisting of both positive and negative charges. [13]

In 1791, Luigi Galvani published his discovery of bioelectromagnetics, demonstrating that electricity was the medium by which neurons passed signals to the muscles. [17] [18] [13] Alessandro Volta's battery, or voltaic pile, of 1800, made from alternating layers of zinc and copper, provided scientists with a more reliable source of electrical energy than the electrostatic machines previously used. [17] [18] The recognition of electromagnetism, the unity of electric and magnetic phenomena, is due to Hans Christian Ørsted and André-Marie Ampère in 1819–1820. Michael Faraday invented the electric motor in 1821, and Georg Ohm mathematically analysed the electrical circuit in 1827. [18] Electricity and magnetism (and light) were definitively linked by James Clerk Maxwell, in particular in his "On Physical Lines of Force" in 1861 and 1862. [19]

While the early 19th century had seen rapid progress in electrical science, the late 19th century would see the greatest progress in electrical engineering. Through such people as Alexander Graham Bell, Ottó Bláthy, Thomas Edison, Galileo Ferraris, Oliver Heaviside, Ányos Jedlik, William Thomson, 1st Baron Kelvin, Charles Algernon Parsons, Werner von Siemens, Joseph Swan, Reginald Fessenden, Nikola Tesla and George Westinghouse, electricity turned from a scientific curiosity into an essential tool for modern life.

In 1887, Heinrich Hertz [20] :843–44 [21] discovered that electrodes illuminated with ultraviolet light create electric sparks more easily. In 1905, Albert Einstein published a paper that explained experimental data from the photoelectric effect as being the result of light energy being carried in discrete quantized packets, energising electrons. This discovery led to the quantum revolution. Einstein was awarded the Nobel Prize in Physics in 1921 for "his discovery of the law of the photoelectric effect". [22] The photoelectric effect is also employed in photocells such as can be found in solar panels and this is frequently used to make electricity commercially.

The first solid-state device was the "cat's-whisker detector" first used in the 1900s in radio receivers. A whisker-like wire is placed lightly in contact with a solid crystal (such as a germanium crystal) to detect a radio signal by the contact junction effect. [23] In a solid-state component, the current is confined to solid elements and compounds engineered specifically to switch and amplify it. Current flow can be understood in two forms: as negatively charged electrons, and as positively charged electron deficiencies called holes. These charges and holes are understood in terms of quantum physics. The building material is most often a crystalline semiconductor. [24] [25]

The solid-state device came into its own with the invention of the transistor in 1947. Common solid-state devices include transistors, microprocessor chips, and RAM. A specialized type of RAM called flash RAM is used in USB flash drives and more recently, solid-state drives to replace mechanically rotating magnetic disc hard disk drives. Solid state devices became prevalent in the 1950s and the 1960s, during the transition from vacuum tubes to semiconductor diodes, transistors, integrated circuit (IC) and the light-emitting diode (LED).

## Concepts

### Electric charge

The presence of charge gives rise to an electrostatic force: charges exert a force on each other, an effect that was known, though not understood, in antiquity. [20] :457 A lightweight ball suspended from a string can be charged by touching it with a glass rod that has itself been charged by rubbing with a cloth. If a similar ball is charged by the same glass rod, it is found to repel the first: the charge acts to force the two balls apart. Two balls that are charged with a rubbed amber rod also repel each other. However, if one ball is charged by the glass rod, and the other by an amber rod, the two balls are found to attract each other. These phenomena were investigated in the late eighteenth century by Charles-Augustin de Coulomb, who deduced that charge manifests itself in two opposing forms. This discovery led to the well-known axiom: like-charged objects repel and opposite-charged objects attract. [20]

The force acts on the charged particles themselves, hence charge has a tendency to spread itself as evenly as possible over a conducting surface. The magnitude of the electromagnetic force, whether attractive or repulsive, is given by Coulomb's law, which relates the force to the product of the charges and has an inverse-square relation to the distance between them. [26] [27] :35 The electromagnetic force is very strong, second only in strength to the strong interaction, [28] but unlike that force it operates over all distances. [29] In comparison with the much weaker gravitational force, the electromagnetic force pushing two electrons apart is 1042 times that of the gravitational attraction pulling them together. [30]

Study has shown that the origin of charge is from certain types of subatomic particles which have the property of electric charge. Electric charge gives rise to and interacts with the electromagnetic force, one of the four fundamental forces of nature. The most familiar carriers of electrical charge are the electron and proton. Experiment has shown charge to be a conserved quantity, that is, the net charge within an electrically isolated system will always remain constant regardless of any changes taking place within that system. [31] Within the system, charge may be transferred between bodies, either by direct contact, or by passing along a conducting material, such as a wire. [27] :2–5 The informal term static electricity refers to the net presence (or 'imbalance') of charge on a body, usually caused when dissimilar materials are rubbed together, transferring charge from one to the other.

The charge on electrons and protons is opposite in sign, hence an amount of charge may be expressed as being either negative or positive. By convention, the charge carried by electrons is deemed negative, and that by protons positive, a custom that originated with the work of Benjamin Franklin. [32] The amount of charge is usually given the symbol Q and expressed in coulombs; [33] each electron carries the same charge of approximately −1.6022×10−19  coulomb. The proton has a charge that is equal and opposite, and thus +1.6022×10−19  coulomb. Charge is possessed not just by matter, but also by antimatter, each antiparticle bearing an equal and opposite charge to its corresponding particle. [34]

Charge can be measured by a number of means, an early instrument being the gold-leaf electroscope, which although still in use for classroom demonstrations, has been superseded by the electronic electrometer. [27] :2–5

### Electric current

The movement of electric charge is known as an electric current, the intensity of which is usually measured in amperes. Current can consist of any moving charged particles; most commonly these are electrons, but any charge in motion constitutes a current. Electric current can flow through some things, electrical conductors, but will not flow through an electrical insulator. [35]

By historical convention, a positive current is defined as having the same direction of flow as any positive charge it contains, or to flow from the most positive part of a circuit to the most negative part. Current defined in this manner is called conventional current. The motion of negatively charged electrons around an electric circuit, one of the most familiar forms of current, is thus deemed positive in the opposite direction to that of the electrons. [36] However, depending on the conditions, an electric current can consist of a flow of charged particles in either direction, or even in both directions at once. The positive-to-negative convention is widely used to simplify this situation.

The process by which electric current passes through a material is termed electrical conduction, and its nature varies with that of the charged particles and the material through which they are travelling. Examples of electric currents include metallic conduction, where electrons flow through a conductor such as metal, and electrolysis, where ions (charged atoms) flow through liquids, or through plasmas such as electrical sparks. While the particles themselves can move quite slowly, sometimes with an average drift velocity only fractions of a millimetre per second, [27] :17 the electric field that drives them itself propagates at close to the speed of light, enabling electrical signals to pass rapidly along wires. [37]

Current causes several observable effects, which historically were the means of recognising its presence. That water could be decomposed by the current from a voltaic pile was discovered by Nicholson and Carlisle in 1800, a process now known as electrolysis. Their work was greatly expanded upon by Michael Faraday in 1833. Current through a resistance causes localised heating, an effect James Prescott Joule studied mathematically in 1840. [27] :23–24 One of the most important discoveries relating to current was made accidentally by Hans Christian Ørsted in 1820, when, while preparing a lecture, he witnessed the current in a wire disturbing the needle of a magnetic compass. [38] He had discovered electromagnetism, a fundamental interaction between electricity and magnetics. The level of electromagnetic emissions generated by electric arcing is high enough to produce electromagnetic interference, which can be detrimental to the workings of adjacent equipment. [39]

In engineering or household applications, current is often described as being either direct current (DC) or alternating current (AC). These terms refer to how the current varies in time. Direct current, as produced by example from a battery and required by most electronic devices, is a unidirectional flow from the positive part of a circuit to the negative. [40] :11 If, as is most common, this flow is carried by electrons, they will be travelling in the opposite direction. Alternating current is any current that reverses direction repeatedly; almost always this takes the form of a sine wave. [40] :206–07 Alternating current thus pulses back and forth within a conductor without the charge moving any net distance over time. The time-averaged value of an alternating current is zero, but it delivers energy in first one direction, and then the reverse. Alternating current is affected by electrical properties that are not observed under steady state direct current, such as inductance and capacitance. [40] :223–25 These properties however can become important when circuitry is subjected to transients, such as when first energised.

### Electric field

The concept of the electric field was introduced by Michael Faraday. An electric field is created by a charged body in the space that surrounds it, and results in a force exerted on any other charges placed within the field. The electric field acts between two charges in a similar manner to the way that the gravitational field acts between two masses, and like it, extends towards infinity and shows an inverse square relationship with distance. [29] However, there is an important difference. Gravity always acts in attraction, drawing two masses together, while the electric field can result in either attraction or repulsion. Since large bodies such as planets generally carry no net charge, the electric field at a distance is usually zero. Thus gravity is the dominant force at distance in the universe, despite being much weaker. [30]

An electric field generally varies in space, [41] and its strength at any one point is defined as the force (per unit charge) that would be felt by a stationary, negligible charge if placed at that point. [20] :469–70 The conceptual charge, termed a 'test charge', must be vanishingly small to prevent its own electric field disturbing the main field and must also be stationary to prevent the effect of magnetic fields. As the electric field is defined in terms of force, and force is a vector, so it follows that an electric field is also a vector, having both magnitude and direction. Specifically, it is a vector field. [20] :469–70

The study of electric fields created by stationary charges is called electrostatics. The field may be visualised by a set of imaginary lines whose direction at any point is the same as that of the field. This concept was introduced by Faraday, [42] whose term 'lines of force' still sometimes sees use. The field lines are the paths that a point positive charge would seek to make as it was forced to move within the field; they are however an imaginary concept with no physical existence, and the field permeates all the intervening space between the lines. [42] Field lines emanating from stationary charges have several key properties: first, that they originate at positive charges and terminate at negative charges; second, that they must enter any good conductor at right angles, and third, that they may never cross nor close in on themselves. [20] :479

A hollow conducting body carries all its charge on its outer surface. The field is therefore zero at all places inside the body. [27] :88 This is the operating principal of the Faraday cage, a conducting metal shell which isolates its interior from outside electrical effects.

The principles of electrostatics are important when designing items of high-voltage equipment. There is a finite limit to the electric field strength that may be withstood by any medium. Beyond this point, electrical breakdown occurs and an electric arc causes flashover between the charged parts. Air, for example, tends to arc across small gaps at electric field strengths which exceed 30 kV per centimetre. Over larger gaps, its breakdown strength is weaker, perhaps 1 kV per centimetre. [43] The most visible natural occurrence of this is lightning, caused when charge becomes separated in the clouds by rising columns of air, and raises the electric field in the air to greater than it can withstand. The voltage of a large lightning cloud may be as high as 100 MV and have discharge energies as great as 250 kWh. [44]

The field strength is greatly affected by nearby conducting objects, and it is particularly intense when it is forced to curve around sharply pointed objects. This principle is exploited in the lightning conductor, the sharp spike of which acts to encourage the lightning stroke to develop there, rather than to the building it serves to protect [45] :155

### Electric potential

The concept of electric potential is closely linked to that of the electric field. A small charge placed within an electric field experiences a force, and to have brought that charge to that point against the force requires work. The electric potential at any point is defined as the energy required to bring a unit test charge from an infinite distance slowly to that point. It is usually measured in volts, and one volt is the potential for which one joule of work must be expended to bring a charge of one coulomb from infinity. [20] :494–98 This definition of potential, while formal, has little practical application, and a more useful concept is that of electric potential difference, and is the energy required to move a unit charge between two specified points. An electric field has the special property that it is conservative , which means that the path taken by the test charge is irrelevant: all paths between two specified points expend the same energy, and thus a unique value for potential difference may be stated. [20] :494–98 The volt is so strongly identified as the unit of choice for measurement and description of electric potential difference that the term voltage sees greater everyday usage.

For practical purposes, it is useful to define a common reference point to which potentials may be expressed and compared. While this could be at infinity, a much more useful reference is the Earth itself, which is assumed to be at the same potential everywhere. This reference point naturally takes the name earth or ground. Earth is assumed to be an infinite source of equal amounts of positive and negative charge, and is therefore electrically uncharged—and unchargeable. [46]

Electric potential is a scalar quantity, that is, it has only magnitude and not direction. It may be viewed as analogous to height: just as a released object will fall through a difference in heights caused by a gravitational field, so a charge will 'fall' across the voltage caused by an electric field. [47] As relief maps show contour lines marking points of equal height, a set of lines marking points of equal potential (known as equipotentials) may be drawn around an electrostatically charged object. The equipotentials cross all lines of force at right angles. They must also lie parallel to a conductor's surface, otherwise this would produce a force that will move the charge carriers to even the potential of the surface.

The electric field was formally defined as the force exerted per unit charge, but the concept of potential allows for a more useful and equivalent definition: the electric field is the local gradient of the electric potential. Usually expressed in volts per metre, the vector direction of the field is the line of greatest slope of potential, and where the equipotentials lie closest together. [27] :60

### Electromagnets

Ørsted's discovery in 1821 that a magnetic field existed around all sides of a wire carrying an electric current indicated that there was a direct relationship between electricity and magnetism. Moreover, the interaction seemed different from gravitational and electrostatic forces, the two forces of nature then known. The force on the compass needle did not direct it to or away from the current-carrying wire, but acted at right angles to it. [38] Ørsted's slightly obscure words were that "the electric conflict acts in a revolving manner." The force also depended on the direction of the current, for if the flow was reversed, then the force did too. [48]

Ørsted did not fully understand his discovery, but he observed the effect was reciprocal: a current exerts a force on a magnet, and a magnetic field exerts a force on a current. The phenomenon was further investigated by Ampère, who discovered that two parallel current-carrying wires exerted a force upon each other: two wires conducting currents in the same direction are attracted to each other, while wires containing currents in opposite directions are forced apart. [49] The interaction is mediated by the magnetic field each current produces and forms the basis for the international definition of the ampere. [49]

This relationship between magnetic fields and currents is extremely important, for it led to Michael Faraday's invention of the electric motor in 1821. Faraday's homopolar motor consisted of a permanent magnet sitting in a pool of mercury. A current was allowed through a wire suspended from a pivot above the magnet and dipped into the mercury. The magnet exerted a tangential force on the wire, making it circle around the magnet for as long as the current was maintained. [50]

Experimentation by Faraday in 1831 revealed that a wire moving perpendicular to a magnetic field developed a potential difference between its ends. Further analysis of this process, known as electromagnetic induction, enabled him to state the principle, now known as Faraday's law of induction, that the potential difference induced in a closed circuit is proportional to the rate of change of magnetic flux through the loop. Exploitation of this discovery enabled him to invent the first electrical generator in 1831, in which he converted the mechanical energy of a rotating copper disc to electrical energy. [50] Faraday's disc was inefficient and of no use as a practical generator, but it showed the possibility of generating electric power using magnetism, a possibility that would be taken up by those that followed on from his work.

### Electrochemistry

The ability of chemical reactions to produce electricity, and conversely the ability of electricity to drive chemical reactions has a wide array of uses.

Electrochemistry has always been an important part of electricity. From the initial invention of the Voltaic pile, electrochemical cells have evolved into the many different types of batteries, electroplating and electrolysis cells. Aluminium is produced in vast quantities this way, and many portable devices are electrically powered using rechargeable cells.

### Electric circuits

An electric circuit is an interconnection of electric components such that electric charge is made to flow along a closed path (a circuit), usually to perform some useful task.

The components in an electric circuit can take many forms, which can include elements such as resistors, capacitors, switches, transformers and electronics. Electronic circuits contain active components, usually semiconductors, and typically exhibit non-linear behaviour, requiring complex analysis. The simplest electric components are those that are termed passive and linear: while they may temporarily store energy, they contain no sources of it, and exhibit linear responses to stimuli. [51] :15–16

The resistor is perhaps the simplest of passive circuit elements: as its name suggests, it resists the current through it, dissipating its energy as heat. The resistance is a consequence of the motion of charge through a conductor: in metals, for example, resistance is primarily due to collisions between electrons and ions. Ohm's law is a basic law of circuit theory, stating that the current passing through a resistance is directly proportional to the potential difference across it. The resistance of most materials is relatively constant over a range of temperatures and currents; materials under these conditions are known as 'ohmic'. The ohm, the unit of resistance, was named in honour of Georg Ohm, and is symbolised by the Greek letter Ω. 1 Ω is the resistance that will produce a potential difference of one volt in response to a current of one amp. [51] :30–35

The capacitor is a development of the Leyden jar and is a device that can store charge, and thereby storing electrical energy in the resulting field. It consists of two conducting plates separated by a thin insulating dielectric layer; in practice, thin metal foils are coiled together, increasing the surface area per unit volume and therefore the capacitance. The unit of capacitance is the farad, named after Michael Faraday, and given the symbol F: one farad is the capacitance that develops a potential difference of one volt when it stores a charge of one coulomb. A capacitor connected to a voltage supply initially causes a current as it accumulates charge; this current will however decay in time as the capacitor fills, eventually falling to zero. A capacitor will therefore not permit a steady state current, but instead blocks it. [51] :216–20

The inductor is a conductor, usually a coil of wire, that stores energy in a magnetic field in response to the current through it. When the current changes, the magnetic field does too, inducing a voltage between the ends of the conductor. The induced voltage is proportional to the time rate of change of the current. The constant of proportionality is termed the inductance. The unit of inductance is the henry, named after Joseph Henry, a contemporary of Faraday. One henry is the inductance that will induce a potential difference of one volt if the current through it changes at a rate of one ampere per second. The inductor's behaviour is in some regards converse to that of the capacitor: it will freely allow an unchanging current, but opposes a rapidly changing one. [51] :226–29

### Electric power

Electric power is the rate at which electric energy is transferred by an electric circuit. The SI unit of power is the watt, one joule per second.

Electric power, like mechanical power, is the rate of doing work, measured in watts, and represented by the letter P. The term wattage is used colloquially to mean "electric power in watts." The electric power in watts produced by an electric current I consisting of a charge of Q coulombs every t seconds passing through an electric potential (voltage) difference of V is

${\displaystyle P={\text{work done per unit time}}={\frac {QV}{t}}=IV\,}$

where

Q is electric charge in coulombs
t is time in seconds
I is electric current in amperes
V is electric potential or voltage in volts

Electricity generation is often done with electric generators, but can also be supplied by chemical sources such as electric batteries or by other means from a wide variety of sources of energy. Electric power is generally supplied to businesses and homes by the electric power industry. Electricity is usually sold by the kilowatt hour (3.6 MJ) which is the product of power in kilowatts multiplied by running time in hours. Electric utilities measure power using electricity meters, which keep a running total of the electric energy delivered to a customer. Unlike fossil fuels, electricity is a low entropy form of energy and can be converted into motion or many other forms of energy with high efficiency. [52]

### Electronics

Electronics deals with electrical circuits that involve active electrical components such as vacuum tubes, transistors, diodes, optoelectronics, sensors and integrated circuits, and associated passive interconnection technologies. The nonlinear behaviour of active components and their ability to control electron flows makes amplification of weak signals possible and electronics is widely used in information processing, telecommunications, and signal processing. The ability of electronic devices to act as switches makes digital information processing possible. Interconnection technologies such as circuit boards, electronics packaging technology, and other varied forms of communication infrastructure complete circuit functionality and transform the mixed components into a regular working system.

Today, most electronic devices use semiconductor components to perform electron control. The study of semiconductor devices and related technology is considered a branch of solid state physics, whereas the design and construction of electronic circuits to solve practical problems come under electronics engineering.

### Electromagnetic wave

Faraday's and Ampère's work showed that a time-varying magnetic field acted as a source of an electric field, and a time-varying electric field was a source of a magnetic field. Thus, when either field is changing in time, then a field of the other is necessarily induced. [20] :696–700 Such a phenomenon has the properties of a wave, and is naturally referred to as an electromagnetic wave. Electromagnetic waves were analysed theoretically by James Clerk Maxwell in 1864. Maxwell developed a set of equations that could unambiguously describe the interrelationship between electric field, magnetic field, electric charge, and electric current. He could moreover prove that such a wave would necessarily travel at the speed of light, and thus light itself was a form of electromagnetic radiation. Maxwell's Laws, which unify light, fields, and charge are one of the great milestones of theoretical physics. [20] :696–700

Thus, the work of many researchers enabled the use of electronics to convert signals into high frequency oscillating currents, and via suitably shaped conductors, electricity permits the transmission and reception of these signals via radio waves over very long distances.

## Production and uses

### Generation and transmission

In the 6th century BC, the Greek philosopher Thales of Miletus experimented with amber rods and these experiments were the first studies into the production of electrical energy. While this method, now known as the triboelectric effect, can lift light objects and generate sparks, it is extremely inefficient. [53] It was not until the invention of the voltaic pile in the eighteenth century that a viable source of electricity became available. The voltaic pile, and its modern descendant, the electrical battery, store energy chemically and make it available on demand in the form of electrical energy. [53] The battery is a versatile and very common power source which is ideally suited to many applications, but its energy storage is finite, and once discharged it must be disposed of or recharged. For large electrical demands electrical energy must be generated and transmitted continuously over conductive transmission lines.

Electrical power is usually generated by electro-mechanical generators driven by steam produced from fossil fuel combustion, or the heat released from nuclear reactions; or from other sources such as kinetic energy extracted from wind or flowing water. The modern steam turbine invented by Sir Charles Parsons in 1884 today generates about 80 percent of the electric power in the world using a variety of heat sources. Such generators bear no resemblance to Faraday's homopolar disc generator of 1831, but they still rely on his electromagnetic principle that a conductor linking a changing magnetic field induces a potential difference across its ends. [54] The invention in the late nineteenth century of the transformer meant that electrical power could be transmitted more efficiently at a higher voltage but lower current. Efficient electrical transmission meant in turn that electricity could be generated at centralised power stations, where it benefited from economies of scale, and then be despatched relatively long distances to where it was needed. [55] [56]

Since electrical energy cannot easily be stored in quantities large enough to meet demands on a national scale, at all times exactly as much must be produced as is required. [55] This requires electricity utilities to make careful predictions of their electrical loads, and maintain constant co-ordination with their power stations. A certain amount of generation must always be held in reserve to cushion an electrical grid against inevitable disturbances and losses.

Demand for electricity grows with great rapidity as a nation modernises and its economy develops. The United States showed a 12% increase in demand during each year of the first three decades of the twentieth century, [57] a rate of growth that is now being experienced by emerging economies such as those of India or China. [58] [59] Historically, the growth rate for electricity demand has outstripped that for other forms of energy. [60] :16

Environmental concerns with electricity generation have led to an increased focus on generation from renewable sources, in particular from wind and hydropower. While debate can be expected to continue over the environmental impact of different means of electricity production, its final form is relatively clean. [60] :89

### Applications

Electricity is a very convenient way to transfer energy, and it has been adapted to a huge, and growing, number of uses. [61] The invention of a practical incandescent light bulb in the 1870s led to lighting becoming one of the first publicly available applications of electrical power. Although electrification brought with it its own dangers, replacing the naked flames of gas lighting greatly reduced fire hazards within homes and factories. [62] Public utilities were set up in many cities targeting the burgeoning market for electrical lighting. In the late 20th century and in modern times, the trend has started to flow in the direction of deregulation in the electrical power sector. [63]

The resistive Joule heating effect employed in filament light bulbs also sees more direct use in electric heating. While this is versatile and controllable, it can be seen as wasteful, since most electrical generation has already required the production of heat at a power station. [64] A number of countries, such as Denmark, have issued legislation restricting or banning the use of resistive electric heating in new buildings. [65] Electricity is however still a highly practical energy source for heating and refrigeration, [66] with air conditioning/heat pumps representing a growing sector for electricity demand for heating and cooling, the effects of which electricity utilities are increasingly obliged to accommodate. [67]

Electricity is used within telecommunications, and indeed the electrical telegraph, demonstrated commercially in 1837 by Cooke and Wheatstone, was one of its earliest applications. With the construction of first intercontinental, and then transatlantic, telegraph systems in the 1860s, electricity had enabled communications in minutes across the globe. Optical fibre and satellite communication have taken a share of the market for communications systems, but electricity can be expected to remain an essential part of the process.

The effects of electromagnetism are most visibly employed in the electric motor, which provides a clean and efficient means of motive power. A stationary motor such as a winch is easily provided with a supply of power, but a motor that moves with its application, such as an electric vehicle, is obliged to either carry along a power source such as a battery, or to collect current from a sliding contact such as a pantograph. Electrically powered vehicles are used in public transportation, such as electric buses and trains, [68] and an increasing number of battery-powered electric cars in private ownership.

Electronic devices make use of the transistor, perhaps one of the most important inventions of the twentieth century, [69] and a fundamental building block of all modern circuitry. A modern integrated circuit may contain several billion miniaturised transistors in a region only a few centimetres square. [70]

## Electricity and the natural world

### Physiological effects

A voltage applied to a human body causes an electric current through the tissues, and although the relationship is non-linear, the greater the voltage, the greater the current. [71] The threshold for perception varies with the supply frequency and with the path of the current, but is about 0.1 mA to 1 mA for mains-frequency electricity, though a current as low as a microamp can be detected as an electrovibration effect under certain conditions. [72] If the current is sufficiently high, it will cause muscle contraction, fibrillation of the heart, and tissue burns. [71] The lack of any visible sign that a conductor is electrified makes electricity a particular hazard. The pain caused by an electric shock can be intense, leading electricity at times to be employed as a method of torture. Death caused by an electric shock is referred to as electrocution. Electrocution is still the means of judicial execution in some jurisdictions, though its use has become rarer in recent times. [73]

### Electrical phenomena in nature

Electricity is not a human invention, and may be observed in several forms in nature, a prominent manifestation of which is lightning. Many interactions familiar at the macroscopic level, such as touch, friction or chemical bonding, are due to interactions between electric fields on the atomic scale. The Earth's magnetic field is thought to arise from a natural dynamo of circulating currents in the planet's core. [74] Certain crystals, such as quartz, or even sugar, generate a potential difference across their faces when subjected to external pressure. [75] This phenomenon is known as piezoelectricity, from the Greek piezein (πιέζειν), meaning to press, and was discovered in 1880 by Pierre and Jacques Curie. The effect is reciprocal, and when a piezoelectric material is subjected to an electric field, a small change in physical dimensions takes place. [75]

§Bioelectrogenesis in microbial life is a prominent phenomenon in soils and sediment ecology resulting from anaerobic respiration. The microbial fuel cell mimics this ubiquitous natural phenomenon.

Some organisms, such as sharks, are able to detect and respond to changes in electric fields, an ability known as electroreception, [76] while others, termed electrogenic, are able to generate voltages themselves to serve as a predatory or defensive weapon. [3] The order Gymnotiformes, of which the best known example is the electric eel, detect or stun their prey via high voltages generated from modified muscle cells called electrocytes. [3] [4] All animals transmit information along their cell membranes with voltage pulses called action potentials, whose functions include communication by the nervous system between neurons and muscles. [77] An electric shock stimulates this system, and causes muscles to contract. [78] Action potentials are also responsible for coordinating activities in certain plants. [77]

## Cultural perception

In the 19th and early 20th century, electricity was not part of the everyday life of many people, even in the industrialised Western world. The popular culture of the time accordingly often depicted it as a mysterious, quasi-magical force that can slay the living, revive the dead or otherwise bend the laws of nature. [80] This attitude began with the 1771 experiments of Luigi Galvani in which the legs of dead frogs were shown to twitch on application of animal electricity. "Revitalization" or resuscitation of apparently dead or drowned persons was reported in the medical literature shortly after Galvani's work. These results were known to Mary Shelley when she authored Frankenstein (1819), although she does not name the method of revitalization of the monster. The revitalization of monsters with electricity later became a stock theme in horror films.

As the public familiarity with electricity as the lifeblood of the Second Industrial Revolution grew, its wielders were more often cast in a positive light, [81] such as the workers who "finger death at their gloves' end as they piece and repiece the living wires" in Rudyard Kipling's 1907 poem Sons of Martha . [81] Electrically powered vehicles of every sort featured large in adventure stories such as those of Jules Verne and the Tom Swift books. [81] The masters of electricity, whether fictional or real—including scientists such as Thomas Edison, Charles Steinmetz or Nikola Tesla—were popularly conceived of as having wizard-like powers. [81]

With electricity ceasing to be a novelty and becoming a necessity of everyday life in the later half of the 20th century, it required particular attention by popular culture only when it stops flowing, [81] an event that usually signals disaster. [81] The people who keep it flowing, such as the nameless hero of Jimmy Webb’s song "Wichita Lineman" (1968), [81] are still often cast as heroic, wizard-like figures. [81]

## Notes

1. Jones, D.A. (1991), "Electrical engineering: the backbone of society", Proceedings of the IEE: Science, Measurement and Technology, 138 (1): 1–10, doi:10.1049/ip-a-3.1991.0001
2. Moller, Peter; Kramer, Bernd (December 1991), "Review: Electric Fish", BioScience, American Institute of Biological Sciences, 41 (11): 794–96 [794], doi:10.2307/1311732, JSTOR   1311732
3. Bullock, Theodore H. (2005), Electroreception, Springer, pp. 5–7, ISBN   0-387-23192-7
4. Morris, Simon C. (2003), Life's Solution: Inevitable Humans in a Lonely Universe, Cambridge University Press, pp. 182–85, ISBN   0-521-82704-3
5. The Encyclopedia Americana; a library of universal knowledge (1918), New York: Encyclopedia Americana Corp
6. Stewart, Joseph (2001), Intermediate Electromagnetic Theory, World Scientific, p. 50, ISBN   981-02-4471-1
7. Simpson, Brian (2003), Electrical Stimulation and the Relief of Pain, Elsevier Health Sciences, pp. 6–7, ISBN   0-444-51258-6
8. Diogenes Laertius. R.D. Hicks, ed. "Lives of Eminent Philosophers, Book 1 Chapter 1 [24]". Perseus Digital Library. Tufts University. Retrieved 5 February 2017. Aristotle and Hippias affirm that, arguing from the magnet and from amber, he attributed a soul or life even to inanimate objects.
9. Aristotle. Daniel C. Stevenson, ed. "De Animus (On the Soul) Book 1 Part 2 (B4 verso)". The Internet Classics Archive. Translated by J.A. Smith. Retrieved 5 February 2017. Thales, too, to judge from what is recorded about him, seems to have held soul to be a motive force, since he said that the magnet has a soul in it because it moves the iron.
10. Frood, Arran (27 February 2003), Riddle of 'Baghdad's batteries', BBC, retrieved 2008-02-16
11. Baigrie, Brian (2007), Electricity and Magnetism: A Historical Perspective, Greenwood Press, pp. 7–8, ISBN   0-313-33358-0
12. Chalmers, Gordon (1937), "The Lodestone and the Understanding of Matter in Seventeenth Century England", Philosophy of Science, 4 (1): 75–95, doi:10.1086/286445
13. Guarnieri, M. (2014). "Electricity in the age of Enlightenment". IEEE Industrial Electronics Magazine. 8 (3): 60–63. doi:10.1109/MIE.2014.2335431.
14. Srodes, James (2002), Franklin: The Essential Founding Father, Regnery Publishing, pp. 92–94, ISBN   0-89526-163-4 It is uncertain if Franklin personally carried out this experiment, but it is popularly attributed to him.
15. Uman, Martin (1987), All About Lightning (PDF), Dover Publications, ISBN   0-486-25237-X
16. Riskin, Jessica (1998), Poor Richard’s Leyden Jar: Electricity and economy in Franklinist France (PDF), p. 327
17. Guarnieri, M. (2014). "The Big Jump from the Legs of a Frog". IEEE Industrial Electronics Magazine. 8 (4): 59–61, 69. doi:10.1109/MIE.2014.2361237.
18. Kirby, Richard S. (1990), Engineering in History, Courier Dover Publications, pp. 331–33, ISBN   0-486-26412-2
19. Berkson, William (1974) Fields of force: the development of a world view from Faraday to Einstein p.148. Routledge, 1974
20. Sears, Francis; et al. (1982), University Physics, Sixth Edition, Addison Wesley, ISBN   0-201-07199-1
21. Hertz, Heinrich (1887). "Ueber den Einfluss des ultravioletten Lichtes auf die electrische Entladung". Annalen der Physik . 267 (8): S. 983–1000. Bibcode:1887AnP...267..983H. doi:10.1002/andp.18872670827.
22. "The Nobel Prize in Physics 1921". Nobel Foundation. Retrieved 2013-03-16.
23. "Solid state", The Free Dictionary
24. John Sydney Blakemore, Solid state physics, pp. 1–3, Cambridge University Press, 1985 ISBN   0-521-31391-0.
25. Richard C. Jaeger, Travis N. Blalock, Microelectronic circuit design, pp. 46–47, McGraw-Hill Professional, 2003 ISBN   0-07-250503-6.
26. "The repulsive force between two small spheres charged with the same type of electricity is inversely proportional to the square of the distance between the centres of the two spheres." Charles-Augustin de Coulomb, Histoire de l'Academie Royal des Sciences, Paris 1785.
27. Duffin, W.J. (1980), Electricity and Magnetism, 3rd edition, McGraw-Hill, ISBN   0-07-084111-X
28. National Research Council (1998), Physics Through the 1990s, National Academies Press, pp. 215–16, ISBN   0-309-03576-7
29. Umashankar, Korada (1989), Introduction to Engineering Electromagnetic Fields, World Scientific, pp. 77–79, ISBN   9971-5-0921-0
30. Hawking, Stephen (1988), A Brief History of Time, Bantam Press, p. 77, ISBN   0-553-17521-1
31. Trefil, James (2003), The Nature of Science: An A–Z Guide to the Laws and Principles Governing Our Universe, Houghton Mifflin Books, p. 74, ISBN   0-618-31938-7
32. Shectman, Jonathan (2003), Groundbreaking Scientific Experiments, Inventions, and Discoveries of the 18th Century, Greenwood Press, pp. 87–91, ISBN   0-313-32015-2
33. Sewell, Tyson (1902), The Elements of Electrical Engineering, Lockwood, p. 18. The Q originally stood for 'quantity of electricity', the term 'electricity' now more commonly expressed as 'charge'.
34. Close, Frank (2007), The New Cosmic Onion: Quarks and the Nature of the Universe, CRC Press, p. 51, ISBN   1-58488-798-2
35. Shock and Awe: The Story of Electricity – Jim Al-Khalili BBC Horizon
36. Ward, Robert (1960), Introduction to Electrical Engineering, Prentice-Hall, p. 18
37. Solymar, L. (1984), Lectures on electromagnetic theory, Oxford University Press, p. 140, ISBN   0-19-856169-5
38. Berkson, William (1974), Fields of Force: The Development of a World View from Faraday to Einstein, Routledge, p. 370, ISBN   0-7100-7626-6 Accounts differ as to whether this was before, during, or after a lecture.
39. "Lab Note #105 EMI Reduction – Unsuppressed vs. Suppressed". Arc Suppression Technologies. April 2011. Retrieved March 7, 2012.
40. Bird, John (2007), Electrical and Electronic Principles and Technology, 3rd edition, Newnes, ISBN   9781417505432
41. Almost all electric fields vary in space. An exception is the electric field surrounding a planar conductor of infinite extent, the field of which is uniform.
42. Morely & Hughes, Principles of Electricity, Fifth edition, p. 73, ISBN   0-582-42629-4
43. Naidu, M.S.; Kamataru, V. (1982), High Voltage Engineering, Tata McGraw-Hill, p. 2, ISBN   0-07-451786-4
44. Naidu, M.S.; Kamataru, V. (1982), High Voltage Engineering, Tata McGraw-Hill, pp. 201–02, ISBN   0-07-451786-4
45. Paul J. Nahin (9 October 2002). Oliver Heaviside: The Life, Work, and Times of an Electrical Genius of the Victorian Age. JHU Press. ISBN   978-0-8018-6909-9.
46. Serway, Raymond A. (2006), Serway's College Physics, Thomson Brooks, p. 500, ISBN   0-534-99724-4
47. Saeli, Sue; MacIsaac, Dan (2007), "Using Gravitational Analogies To Introduce Elementary Electrical Field Theory Concepts", The Physics Teacher, 45 (2): 104, Bibcode:2007PhTea..45..104S, doi:10.1119/1.2432088 , retrieved 2007-12-09
48. Thompson, Silvanus P. (2004), Michael Faraday: His Life and Work, Elibron Classics, p. 79, ISBN   1-4212-7387-X
49. Morely & Hughes, Principles of Electricity, Fifth edition, pp. 92–93
50. Institution of Engineering and Technology, Michael Faraday: Biography, archived from the original on 2007-07-03, retrieved 2007-12-09
51. Alexander, Charles; Sadiku, Matthew (2006), Fundamentals of Electric Circuits (3, revised ed.), McGraw-Hill, ISBN   9780073301150
52. Environmental Physics By Clare Smith 2001
53. Dell, Ronald; Rand, David (2001), "Understanding Batteries", Unknown, Royal Society of Chemistry, 86: 2–4, Bibcode:1985STIN...8619754M, ISBN   0-85404-605-4
54. McLaren, Peter G. (1984), Elementary Electric Power and Machines, Ellis Horwood, pp. 182–83, ISBN   0-85312-269-5
55. Patterson, Walter C. (1999), Transforming Electricity: The Coming Generation of Change, Earthscan, pp. 44–48, ISBN   1-85383-341-X
56. Edison Electric Institute, History of the Electric Power Industry, archived from the original on November 13, 2007, retrieved 2007-12-08
57. Edison Electric Institute, History of the U.S. Electric Power Industry, 1882–1991 , retrieved 2007-12-08
58. Carbon Sequestration Leadership Forum, An Energy Summary of India, archived from the original on 2007-12-05, retrieved 2007-12-08
59. IndexMundi, China Electricity – consumption , retrieved 2007-12-08
60. National Research Council (1986), Electricity in Economic Growth, National Academies Press, ISBN   0-309-03677-1
61. Wald, Matthew (21 March 1990), "Growing Use of Electricity Raises Questions on Supply", New York Times, retrieved 2007-12-09
62. d'Alroy Jones, Peter, The Consumer Society: A History of American Capitalism, Penguin Books, p. 211
63. "The Bumpy Road to Energy Deregulation". EnPowered. 2016-03-28.
64. ReVelle, Charles and Penelope (1992), The Global Environment: Securing a Sustainable Future, Jones & Bartlett, p. 298, ISBN   0-86720-321-8
65. Danish Ministry of Environment and Energy, "F.2 The Heat Supply Act", Denmark's Second National Communication on Climate Change, archived from the original on January 8, 2008, retrieved 2007-12-09
66. Brown, Charles E. (2002), Power resources, Springer, ISBN   3-540-42634-5
67. Hojjati, B.; Battles, S., The Growth in Electricity Demand in U.S. Households, 1981–2001: Implications for Carbon Emissions (PDF), archived from the original (PDF) on 2008-02-16, retrieved 2007-12-09
68. "Public Transportation", Alternative Energy News, 2010-03-10
69. Herrick, Dennis F. (2003), Media Management in the Age of Giants: Business Dynamics of Journalism, Blackwell Publishing, ISBN   0-8138-1699-8
70. Das, Saswato R. (2007-12-15), "The tiny, mighty transistor", Los Angeles Times
71. Tleis, Nasser (2008), Power System Modelling and Fault Analysis, Elsevier, pp. 552–54, ISBN   978-0-7506-8074-5
72. Grimnes, Sverre (2000), Bioimpedance and Bioelectricity Basic, Academic Press, pp. 301–09, ISBN   0-12-303260-1
73. Lipschultz, J.H.; Hilt, M.L.J.H. (2002), Crime and Local Television News, Lawrence Erlbaum Associates, p. 95, ISBN   0-8058-3620-9
74. Encrenaz, Thérèse (2004), The Solar System, Springer, p. 217, ISBN   3-540-00241-3
75. Lima-de-Faria, José; Buerger, Martin J. (1990), "Historical Atlas of Crystallography", Zeitschrift für Kristallographie, Springer, 209 (12): 67, Bibcode:1994ZK....209.1008P, doi:10.1524/zkri.1994.209.12.1008a, ISBN   0-7923-0649-X
76. Ivancevic, Vladimir & Tijana (2005), Natural Biodynamics, World Scientific, p. 602, ISBN   981-256-534-5
77. Kandel, E.; Schwartz, J.; Jessell, T. (2000), Principles of Neural Science, McGraw-Hill Professional, pp. 27–28, ISBN   0-8385-7701-6
78. Davidovits, Paul (2007), Physics in Biology and Medicine, Academic Press, pp. 204–05, ISBN   978-0-12-369411-9
79. Jackson, Mark (4 November 2013), Theoretical physics – like sex, but with no need to experiment, The Conversation
80. Van Riper, A. Bowdoin (2002), Science in popular culture: a reference guide, Westport: Greenwood Press, p. 69, ISBN   0-313-31822-0
81. Van Riper, op.cit., p. 71.

## Related Research Articles

The ampere, often shortened to "amp", is the base unit of electric current in the International System of Units (SI). It is named after André-Marie Ampère (1775–1836), French mathematician and physicist, considered the father of electrodynamics.

Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles. The electromagnetic force usually exhibits electromagnetic fields such as electric fields, magnetic fields, and light, and is one of the four fundamental interactions in nature. The other three fundamental interactions are the strong interaction, the weak interaction, and gravitation. At high energy the weak force and electromagnetic force are unified as a single electroweak force.

An electromagnetic field is a physical field produced by electrically charged objects. It affects the behavior of charged objects in the vicinity of the field. The electromagnetic field extends indefinitely throughout space and describes the electromagnetic interaction. It is one of the four fundamental forces of nature.

In physics the Lorentz force is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge q moving with a velocity v in an electric field E and a magnetic field B experiences a force of

Voltage, electric potential difference, electric pressure or electric tension is the difference in electric potential between two points. The difference in electric potential between two points in a static electric field is defined as the work needed per unit of charge to move a test charge between the two points. In the International System of Units, the derived unit for voltage is named volt. In SI units, work per unit charge is expressed as joules per coulomb, where 1 volt = 1 joule per 1 coulomb. The official SI definition for volt uses power and current, where 1 volt = 1 watt per 1 ampere. This definition is equivalent to the more commonly used 'joules per coulomb'. Voltage or electric potential difference is denoted symbolically by V, but more often simply as V, for instance in the context of Ohm's or Kirchhoff's circuit laws.

Electromagnetic or magnetic induction is the production of an electromotive force across an electrical conductor in a changing magnetic field.

Electromotive force, abbreviated emf, is the electrical intensity or "pressure" developed by a source of electrical energy such as a battery or generator. A device that converts other forms of energy into electrical energy provides an emf as its output.

In electricity generation, a generator is a device that converts motive power into electrical power for use in an external circuit. Sources of mechanical energy include steam turbines, gas turbines, water turbines, internal combustion engines and even hand cranks. The first electromagnetic generator, the Faraday disk, was invented in 1831 by British scientist Michael Faraday. Generators provide nearly all of the power for electric power grids.

Electrostatics is a branch of physics that studies electric charges at rest.

Electrostatic induction, also known as "electrostatic influence" or simply "influence" in Europe and Latin America, is a redistribution of electrical charge in an object, caused by the influence of nearby charges. In the presence of a charged body, an insulated conductor develops a positive charge on one end and a negative charge on the other end. Induction was discovered by British scientist John Canton in 1753 and Swedish professor Johan Carl Wilcke in 1762. Electrostatic generators, such as the Wimshurst machine, the Van de Graaff generator and the electrophorus, use this principle. Due to induction, the electrostatic potential (voltage) is constant at any point throughout a conductor. Electrostatic Induction is also responsible for the attraction of light nonconductive objects, such as balloons, paper or styrofoam scraps, to static electric charges. Electrostatic induction laws apply in dynamic situations as far as the quasistatic approximation is valid. Electrostatic induction should not be confused with Electromagnetic induction.

A homopolar generator is a DC electrical generator comprising an electrically conductive disc or cylinder rotating in a plane perpendicular to a uniform static magnetic field. A potential difference is created between the center of the disc and the rim with an electrical polarity that depends on the direction of rotation and the orientation of the field. It is also known as a unipolar generator, acyclic generator, disk dynamo, or Faraday disc. The voltage is typically low, on the order of a few volts in the case of small demonstration models, but large research generators can produce hundreds of volts, and some systems have multiple generators in series to produce an even larger voltage. They are unusual in that they can source tremendous electric current, some more than a million amperes, because the homopolar generator can be made to have very low internal resistance.

The history of electromagnetic theory begins with ancient measures to understand atmospheric electricity, in particular lightning. People then had little understanding of electricity, and were unable to explain the phenomena. Scientific understanding into the nature of electricity grew throughout the eighteenth and nineteenth centuries through the work of researchers such as Ampère, Coulomb, Faraday and Maxwell.

A dynamo is an electrical generator that creates direct current using a commutator. Dynamos were the first electrical generators capable of delivering power for industry, and the foundation upon which many other later electric-power conversion devices were based, including the electric motor, the alternating-current alternator, and the rotary converter. Today, the simpler alternator dominates large scale power generation, for efficiency, reliability and cost reasons. A dynamo has the disadvantages of a mechanical commutator. Also, converting alternating to direct current using power rectification devices is effective and usually economical.

Most of the terms listed in Wikipedia glossaries are already defined and explained within Wikipedia itself. However, glossaries like this one are useful for looking up, comparing and reviewing large numbers of terms together. You can help enhance this page by adding new terms or writing definitions for existing ones.

Electromagnetism is the study of interactions between particles and the electromagnetic field. It includes the study of forces between charged particles, electromagnetic fields and potential, the behavior of conductors and insulators in fields, circuits, magnetism, and electromagnetic waves. An understanding of electromagnetism is important for practical applications like electrical engineering and chemistry. In addition, concepts taught in courses on electromagnetism provide a basis for more advanced material in physics, such as quantum field theory and general relativity. This article focuses on a conceptual understanding of the topics rather than the details of the mathematics involved.

## References

Media related to Electricity at Wikimedia Commons