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several questions in electromagnetics

I went through the book of engineering electromagnetics and I have several questions I dont understand.

1. If the line integral of electrical field is not zero at the existence of changing magnetic field, then how can KVL holds with AC current flowing in the circuit? I do not know what's wrong with my understanding. Isnt AC current generates changing magnetic field at the surface of the circuit, which generates non-zero integral of electrical field along the line path and contradict with KVL?

2. The book mentions about that conduction current density J= σE is the motion of charge in a region of zero net charge density and convection current density J=ρv is the motion of volume charge density. I couldnt understand because the formula of conduction current density J= σE is derived from the one of convection current density J=ρv. Ok, if they are different, would you please give me specific examples about what conduction current is and what convection current is. Personally I thought they were just conduction current.

3. I really couldnt understand the boundary conditions Etangential1=Etangential2 and Htangential1=Htangential2 of time-varying fields. Where do partialB/partialT and partialD/partialT go? Isnt it time-varying fields and shouldnt these two terms be zero? The book says that they should be zero between any two real physical media but also mentions that surface charge density is physical possible for either dielectrics, perfect conductors or imperfect conductors and surface current density for perfect conductors. I am confused. If surface charge density and surface current density are possible, why should these two terms be zero?

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I have time to answer one tonight. I'll be back tomorrow if no one else chimes in.  1 - You are astute to notice that KVL appears to be violated in the case of AC circuit. Time varying current flowing in the wires causes time varying magnetic field (amperes law). According to Maxwell's Eqn. this should cause the EMF around the loop to be non-zero.  Here is how we get around this problem.  1 - We pretend that the wires do not create the aformentioned magnetic fields. 2 - Gather up all of the magnetic flux that should have been generated by the wires and assign it to an inductor that we insert into the circuit. We call this the circuit's "parastic inductance". 3 - The parastic inductor now carries all of the Maxwell's eqn. voltage drop so that we can still say that the EMF around the circuit is zero.  Sometimes we break the parasitic inductance into several parts, each cooresponding to a section of the wires. In this case they are called "partial inductances".

Hey many thanks for your answer and it reminds me the model of transmission line. It is clear for me now.

several questions in electromagnetics

Those are very good question, I can answer #3 right off my head:

For line integral of E:

$$\int_s \nabla X \vec E\cdot d\vec s=\int_c \vec E\cdot d\vec l=-\int_s\frac{\partial \vec B}{\partial t} \cdot d\vec s$$

Remember the closed loop rectangle in the boundary condition? As the length of two sides that is normal to the surface approach zero, the area inside the loop approach zero

$$\int_s\frac{\partial \vec B}{\partial t} \cdot d\vec s \;\rightarrow \;0$$

So the term disappeared. Therefore

$$\int_s \nabla X \vec E\cdot d\vec s=\int_c \vec E\cdot d\vec l=0$$

This reasoning is the same for the magnetic boundary condition.

One thing very important, when you get down to it, time varying signal travels as EM wave, not as current. electrons move very slow, it's the EM wave that travels at close to light speed. The current you measure is really due to the boundary condition of the EM wave........namely

$$\int_s \nabla X \vec H \cdot d\vec s = \int_s \vec J \cdot d\vec s$$

Where J is surface current at the boundary surface.

Also you have to be careful about looking at KVL for everything. There was a big debate on a professor of MIT proving KVL don't hold in magnetic induction. In EE, people use equivalent circuits, using KVL, Thevenin, Norton, super position etc. They don't necessary hold in physics. If you are interested, read this long post. I spent my whole Christmas holiday on this and more.

http://www.physicsforums.com/showthr...3575&highlight

Quote by CheyenneXia 					 				 				2. The book mentions about that conduction current density J= σE is the motion of charge in a region of zero net charge density and convection current density J=ρv is the motion of volume charge density. I couldnt understand because the formula of conduction current density J= σE is derived from the one of convection current density J=ρv. Ok, if they are different, would you please give me specific examples about what conduction current is and what convection current is. Personally I thought they were just conduction current.
I did some digging as convection current is less common than conduction current, I have to read up on it. This is my understanding:

Convection current mainly talking about actual charge particles moving in vacuum. The velocity is more governed by Newton force F=ma where F is eE. The velocity obey the Newton's law where du/dR=a ( u is velocity, R is displacement, a is acceleration.). Then ρ=-J/u.

For conduction current, it is really electrons jumping from one atom to the next atom of a conductive material under the electric field applied. At any given time, there is no net charge in any atom inside the conductive material. The velocity is governed by both E and the mobility $\mu_e\;$ of the conductive material where $\vec u =\mu_e\;\vec E$. In conduction, $\rho=\mu_e\vec E$. The velocity is very slow, the better the conductor, the slower the velocity is. I think it's because the electron keep hitting the atoms like a pin ball machine!!! It never gain velocity......at least this is my guessing.

The two might use the same symbol, but the mechanism is very different. This is just my understanding.

BTW, Electromagnetics is a very difficult subject. It is like peeling an onion, you have layer after layer. You peel one layer and you might think you understand. Then you read again, then you discover you have more question than answer. Then you study, and you peel another layer.....and so on. I studied three different times with three different books. I only feel good..........if I don't open the book and look at it. If I open the book, then I start to ask question and I have no idea how to explain it.

I just post a question something related to how current travel that I thought I understand. But upon reading over, something really missing and I posted in the Classical physics forum here. I got no answer. If someone here have an answer, please join in.

http://www.physicsforums.com/showthr...6127&highlight

Sorry to be the only one that post on this thread, by the time I thought of something, it's too late to edit my last post!!!  I have been thinking about the first question and the big debate I had about the MIT professor Levin. The lesson I learned from the debate is a lot of theorems in electronics don't necessary stand the test of physics. For example, we use super position and super impost two separate circuits together to become one. We use it so much that we kind of take it as the LAW. But in physical world, there is no two circuit. Like Thevinin, we replace parallel resistor with a series resistor and create a equiv Vth. That does not hold up in physical world.  I am not comfortable to explain using "consider there is two sources, one doing......, the other doing......." or even explain EM wave propagation by those 5 balls hanging on strings and if you swing one ball to hit on the right side, the left most ball bounce up immediately. Because in physical world, I don't think this is the physics.  I did some thinking and digging. The reason KVL call into question and not working out in circuit in varying magnetic field is because E is no longer conservative. Remember the definition of conservative field? A conservative field is a Gradient of a scalar function. If E is conservative,   $$\vec E=-\nabla V \;\hbox { where }\; V \; \hbox{ is some scalar function.}$$ Also: $$\vec E=-\nabla V \;\Rightarrow\; \nabla X \vec E= 0,\;\hbox{ which implies E is Irrotational.}$$  Remember $\nabla X \vec E=0$ means the closed loop of a conservative field is zero. This is same as the difinition of KVL. KVL only work in static condition where the E is conservative field.  But in Maxwell's equation for varying field:  $$\nabla X \vec E =-\frac {\partial \vec B}{\partial t}$$  It is no longer conservative, therefore KVL have issue.  I know this is not the best explanation, I know it would be so much simpler to use equivalent circuits and all. That's the reason I was ranting about the theorem vs law. This post is more about me finally moving a step forward in understanding the debate of the MIT professor that I spent a month typing.  Anyone have different idea, please join in, this is only my revelation of the day, peeling one layer of the onion......hopefully.

Recognitions:
Science Advisor

Quote by yungman 					 				 				For conduction current, it is really electrons jumping from one atom to the next atom of a conductive material under the electric field applied. At any given time, there is no net charge in any atom inside the conductive material. The velocity is governed by both E and the mobility $\mu_e\;$ of the conductive material where $\vec u =\mu_e\;\vec E$. In conduction, $\rho=\mu_e\vec E$. The velocity is very slow, the better the conductor, the slower the velocity is. I think it's because the electron keep hitting the atoms like a pin ball machine!!! It never gain velocity......at least this is my guessing.
This post contains numerous errors. Electrons do not jump from atom to atom, they are in the metallic crystal's conduction band where they act as an "electron gas". The electron drift velocity is usually directly proportional to electric field. Better conductors do not have "slower" electrons, I don't even know what this means. Better conductors have fewer scattering defects, hence a longer mean free path between collisions, which results in higher net drift velocity.

There are also misconceptions in other posts in this thread. Caveat emptor, beware...

Quote by marcusl 					 				 				This post contains numerous errors. Electrons do not jump from atom to atom, they are in the metallic crystal's conduction band where they act as an "electron gas". The electron drift velocity is usually directly proportional to electric field. Better conductors do not have "slower" electrons, I don't even know what this means. Better conductors have fewer scattering defects, hence a longer mean free path between collisions, which results in higher net drift velocity.  There are also misconceptions in other posts in this thread. Caveat emptor, beware...
Electrons in the outer valency band of the conductor do move around loosely. The total net charge is zero but yes the electrons do move from one atom to the other. This is in the books about conduction electrons. You can call it jump or a conduction cloud as electrons of the outer band move freely from one atom to another and they do fall back into the valency band of the atom occasionally. How ever which way you call it, they move around.

Please correct any misconceptions in my post here. I would like to learn.

I read my post #6 again, I should be more specific about the theorem, that it is my impression, opinion and observation only. I am not a theoretician, that's the reason I did say people please join in the last sentence.   The over one month of typing in the thread debating about the validity of KVL in the MIT professor's video really get me thinking about those theorems in EE. I was using equivalent voltage source and equivalent circuit in magnetic induction.....which went nowhere.  I love to hear others opinions.

Recognitions:      Gold Member        Science  Advisor  I saw this video   http://www.youtube.com/watch?v=EwIk2gew-R8 some time ago and decided it's sophistry.  emi guy answered it - electrmagnetically  induced voltage is another siource and must be included in any correct implementation of kirchoff's method.   Including the voltmeter leads.  at least to my simple , alleged mind  old jim

Quote by jim hardy 					 				 				I saw this video   http://www.youtube.com/watch?v=EwIk2gew-R8 some time ago and decided it's sophistry.  emi guy answered it - electrmagnetically  induced voltage is another siource and must be included in any correct implementation of kirchoff's method.   Including the voltmeter leads.  at least to my simple , alleged mind  old jim
Ha ha, that's what was exactly what I based on to argue and I really spent the whole Christmas typing and debating two years ago!!! I was absolutely out theory by those people, I finally gave up because they site too many articles and it's over my head.

If you go through the long thread, I actually did experiment and took picture and drew equivalent circuits to support my argument.
http://www.physicsforums.com/showthr...3575&highlight

If you go to page 14 post 224, you'll see the pictures and the argument I put out. I even show holding the probe steady at the same point, and I can change the reading on the scope just by swinging the ground lead of the probe in different position. I even analyzed and explained the reason with drawing of the ground lead of the probe, showing that the EMF was induced onto the ground lead of the probe that cause the reading to change.

Anyone have a better theory, go revive that thread, I love to be vindicated from that!!!

Quote by marcusl 					 				 				This post contains numerous errors. Electrons do not jump from atom to atom, they are in the metallic crystal's conduction band where they act as an "electron gas". The electron drift velocity is usually directly proportional to electric field. Better conductors do not have "slower" electrons, I don't even know what this means. Better conductors have fewer scattering defects, hence a longer mean free path between collisions, which results in higher net drift velocity.  There are also misconceptions in other posts in this thread. Caveat emptor, beware...
Can you please point out where is my error? It is important for me and others to know.

As for velocity, good conductors like Ag, Cu, Ag and Al have mobility of 6EE-3 to 1.4EE-4. But if you look at Si and Ge where it is not as good a conductor, mobility is 0.14 and 0.32. They are higher.

$$\vec u= \mu_e \vec E.$$

So given the same current, velocity is higher with Si and Ge according to the formula. AND also, Si and Ge has much lower conductivity, it will takes higher E to get the same current. So both point to higher velocity for Si and Ge compare to the good conductors.

I further question the limitation of Ohm's Law, I even posted a specific example that Ohm's Law can not accommodate in the Classical Physics forum and looks like there is a limitation:

http://www.physicsforums.com/showthread.php?t=659307

This has nothing to do with magnetic induction and conservative field, more to do with the EM propagation of the signal rather than current and voltage. Feel free to join in the other post.

Thank you. I know why I was confused. Surface current density exists but no surface time-varying field densities. Time varying field exisits in 3D.

Quote by yungman 					 				 				Those are very good question, I can answer #3 right off my head:  For line integral of E:  $$\int_s \nabla X \vec E\cdot d\vec s=\int_c \vec E\cdot d\vec l=-\int_s\frac{\partial \vec B}{\partial t} \cdot d\vec s$$  Remember the closed loop rectangle in the boundary condition? As the length of two sides that is normal to the surface approach zero, the area inside the loop approach zero  $$\int_s\frac{\partial \vec B}{\partial t} \cdot d\vec s \;\rightarrow \;0$$  So the term disappeared. Therefore   $$\int_s \nabla X \vec E\cdot d\vec s=\int_c \vec E\cdot d\vec l=0$$  This reasoning is the same for the magnetic boundary condition.  One thing very important, when you get down to it, time varying signal travels as EM wave, not as current. electrons move very slow, it's the EM wave that travels at close to light speed. The current you measure is really due to the boundary condition of the EM wave........namely  $$\int_s \nabla X \vec H \cdot d\vec s = \int_s \vec J \cdot d\vec s$$  Where J is surface current at the boundary surface.   Also you have to be careful about looking at KVL for everything. There was a big debate on a professor of MIT proving KVL don't hold in magnetic induction. In EE, people use equivalent circuits, using KVL, Thevenin, Norton, super position etc. They don't necessary hold in physics. If you are interested, read this long post. I spent my whole Christmas holiday on this and more.  http://www.physicsforums.com/showthr...3575&highlight

I am more and more confused. I guess I should get a book related to electronic materials and read some charpters on conductor.

Thanks.

Quote by yungman 					 				 				Can you please point out where is my error? It is important for me and others to know.  As for velocity, good conductors like Ag, Cu, Ag and Al have mobility of 6EE-3 to 1.4EE-4. But if you look at Si and Ge where it is not as good a conductor, mobility is 0.14 and 0.32. They are higher.   $$\vec u= \mu_e \vec E.$$  So given the same current, velocity is higher with Si and Ge according to the formula. AND also, Si and Ge has much lower conductivity, it will takes higher E to get the same current. So both point to higher velocity for Si and Ge compare to the good conductors.  I further question the limitation of Ohm's Law, I even posted a specific example that Ohm's Law can not accommodate in the Classical Physics forum and looks like there is a limitation:  http://www.physicsforums.com/showthread.php?t=659307  This has nothing to do with magnetic induction and conservative field, more to do with the EM propagation of the signal rather than current and voltage. Feel free to join in the other post.

Quote by CheyenneXia 					 				 				Thank you. I know why I was confused. Surface current density exists but no surface time-varying field densities. Time varying field exisits in 3D.  As for your post about skin effect, I do not really get your question. Sorry.
If you look at the drawing......which is a more detail version with color of a diagram from "Field and Wave Electromagnetics" by David K Cheng. There are two sources of current, one is the surface current from the curl of H, that explain directly where the current comes from. BUT there is another source of current arise from the Divergence of E where

$$\nabla \cdot \vec D= \rho_{free}$$

You can see the charge as "+" and "-" at the boundary of the two plates. There is no account of this free charges that I can find in any books.

Also about the skin effect. We know skin effect is just a definition of the thickness of a number times $e^{-1}$. The important thing is even at lower frequency, signal travels as EM wave. At low frequency, skin depth is very deep, not just surface current like the boundary condition indicates. How do you account the skin depth when all the Maxwell's equation is about surface current.

Hope I don't confuse you more.

Quote by CheyenneXia 					 				 				I am more and more confused. I guess I should get a book related to electronic materials and read some charpters on conductor.  Thanks.
I came up with a case to challenge the validity of Ohm's Law using an example of microstrip transmission line. As I repeat many times, time varying signal travels as EM wave, not as current and voltage. The case I presented cannot be explained by Ohm's Law that electronic people hold on so dearly. Just like what you so wisely asked about the problem with KVL in the presence of magnetic field. In my example, it is not related to magnetic induction like in your case, it is related to signal travels as EM wave, not current and voltage. This really does not have a lot to do with electronic materials, as long as it is a good conductor, it will behave like this.

Electromagnetic is the most difficult subject in EE by a mile. People spend their live time studying and it's mostly peeling onions. Some manage to peel more layers and some don't. I answer your question to the best of my knowledge, but I cannot be absolutely sure I am right. When Marcusl claimed I made misguided statements in many occasions in this thread, I really want to know so I can look at it, judge the validity and learn. I know I made statement that is quite out there, but I rather speak what I think I understand so people can come back and say whether it's right or wrong. I don't want to just keep quiet on things that I believe is right so I won't be called out. That's the only way to learn......keep peeling the onion.

You should read some of the post in the MIT professor Levin's thread, there are a lot of info that you might be interested. I have to say after spending all the time debating there, I really starting to see things their way........That you have to distinguish an equivalent circuit vs a general law. That I really hesitant to use "think of it as if......". You want to understand EM, my best advice is to really get good at vector calculus, line integral, divergence and curl. Each of them really mean something, just like English sentences. The original Maxwell's equations are INTERPRETED by vector calculus, use calculus to explain it, don't just rely on equivalent circuits. That's the original words. Vector calculus is the language of EM, learn the language.

Quote by jim hardy 					 				 				I saw this video   http://www.youtube.com/watch?v=EwIk2gew-R8 some time ago and decided it's sophistry.  emi guy answered it - electrmagnetically  induced voltage is another siource and must be included in any correct implementation of kirchoff's method.   Including the voltmeter leads.  at least to my simple , alleged mind  old jim
I watched this video in dismay. "Sophistry" is exactly the right word.

When he introduces his time-varying magnetic flux he no longer has a 2 node circuit consisting of two resistors.
He will have two resistors and induced voltage sources adding up to 1V in the equivalent circuit. This is at least three nodes.
He is showing only two nodes (A and D) even after magnetic induction is creating emf across the wires.

- Do we insert an induced 1V source in series with the top wire (splitting node D into two nodes)?
- Do we insert an induced 1V source in series with the bottom wire (splitting node A into two nodes)?
- Do we divide up the voltage drop by adding sources on both top and bottom?

Turns out you can't tell because the problem itself is *defective*.
He shows magnetic flux leaving the blackboard inside of the circuit loop (arrowheads) but he does not show how the flux returns back *into* the blackboard (feathers).

In other words he is employing a fictional magnetic monopole to make his argument.

Magnetic flux must always flow in closed loops, and it is the details of their complete loops, which he has omitted, which allows us to construct the correct equivalent circuit for application of Kirchoff's circuit laws.

For example, if he was using a U-core to pipe magnetic flux into the circuit loop from the top (around the D wire) then we are inducing 1V across the top wire.
The circuit would be drawn to include a voltage source between the top ends of the resistors (three node circuit).

If he was using an E-core to pipe flux into the center from around both wires then the induced voltage will be split between top and bottom wires in proportion to the quantity of flux taking each path (4 node circuit).

If he used a radially symmetrical pot-core, we would have sources equal to half of the induced voltage in series with both top and bottom wires.

I would hope that this was part 1 of a two part lecture and that the students were given the full picture in the next class after pondering it for a few days.

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