# Several questions in electromagnetics

yungman - i don't do well at higher math.

But i did think Levin was mis-applying KVL when he ignored some induction.

Where's that thread ? - i'll see if i can get my alleged brain around it

but be advised - in math skills i dont even come up to your knees.

isn't that Lenz's law - it'll try to make the current oppose the changing flux?
And what do you mean "at the given voltage"?

old jim

This is related to this post:

The return current path follow right under the trace no matter how you snake the trace around.

marcusl
Gold Member
I will expand on the technical issues that I alluded to before, then address some additional issues.
1) The reason that the integral of $$\oint_c \vec E\cdot d\vec l$$ is zero is not that the area of the path goes to zero. It is zero because the line integral of E parallel to and on the outside of the boundary separating material 1 from 2 becomes equal and opposite to that along the inside of the boundary, as the separation between the two paths approaches zero. Thus the two contributions cancel.

2) In the last integral in post #4, J is current density, not surface current as you state; it is allowed to cross the boundary, and it does not have the dimensions of surface current density. Your discussion about EM waves seems to have little direct relevance to the question, furthermore.
Evaluating the integral gives $$\vec{J}\cdot\vec{m} \Delta l = \vec{K}\cdot\vec{m},$$ where K is surface current density and m is the normal to the surface that is bounded by the integration curve. This equation gives rise to the boundary condition on H_tangential that the original poster asked about, namely $$\vec{n}\times(\vec{H_2} - \vec{H_1})=\vec{K} .$$
3) Conduction does not occur by electrons jumping from one atom to the next.

4) Current (or conduction) is always spoken of as being driven ultimately by potential energy differences. Hence current in a charge-neutral wire is the gradient of a potential, leading to Ohm’s law being written $$\vec{J}=\sigma \vec{E}$$ rather than the other way around. Furthermore, we always measure "I-V" curves where V is the independent variable. As a result, drift velocity increases in copper samples of greater purity and decreases in dirtier samples.

5) Post 6 gives a rather roundabout argument that a time-invariant form of Kirchoff’s laws cannot be applied to a time varying circuit. This, of course, merely restates the condition that gave rise to the original question. The answer to the question is to form Kirchoff’s laws to include the time-varying terms in Maxwell’s equations. Including dB/dt introduces into the circuit some emf’s due to self and mutual induction, as the_emi_guy has already pointed out. Including dD/dt allows the treatment of displacement currents in capacitors.

6) “Electromagnetic is the most difficult subject in EE by a mile.” There are topics (stability of a system, information capacity of a multipath scattering communication channel, maximum entropy spectral analysis, error correction coding, etc.) that others could claim are much more difficult than the problems we are dealing with here.

yungman, I have asked you in previous threads not to post erroneous answers in areas where you are not an expert. You state here, instead, that you post what you like and want other people to correct you, and that you like to argue with the corrections. This is counterproductive from many standpoints. I'll give three:
1. It is tedious for those (myself in this case, others in previous threads of yours) whom you expect to a) wade through your voluminous posts, b) try to correct your errors and misconceptions, and c) then argue with you.
2. You spread confusion and misinformation. In this case, you confused the original poster CheyenneXia, at the very least.
3. You undermine your own credibility, and also make it less likely that experts will be interested in engaging with you.

I believe restraint is the better approach.

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berkeman
Mentor
Your concerns are valid marcusl. Sorry yungman, please take his feedback to heart.

marcusl
Gold Member
Also I'll point out that you have completely hijacked this thread so it is focused on a topic taken from your own, different thread.

I will expand on the technical issues that I alluded to before, then address some additional issues.
1) The reason that the integral of $$\oint_c \vec E\cdot d\vec l$$ is zero is not that the area of the path goes to zero. It is zero because the line integral of E parallel to and on the outside of the boundary separating material 1 from 2 becomes equal and opposite to that along the inside of the boundary, as the separation between the two paths approaches zero. Thus the two contributions cancel.

It is the integration around a closed path is ZERO in a conservative field.

http://en.wikipedia.org/wiki/Conservative_field.

And under magnetic induction, the E field is no longer conservative. Watch the Professor Lavine's discussion on this. This is written in page 309 of Field and Wave Electromagnetics by David K Cheng.

https://www.amazon.com/dp/0201128195/?tag=pfamazon01-20

2) In the last integral in post #4, J is current density, not surface current as you state; it is allowed to cross the boundary, and it does not have the dimensions of surface current density. Your discussion about EM waves seems to have little direct relevance to the question, furthermore.
Evaluating the integral gives $$\vec{J}\cdot\vec{m} \Delta l = \vec{K}\cdot\vec{m},$$ where K is surface current density and m is the normal to the surface that is bounded by the integration curve. This equation gives rise to the boundary condition on H_tangential that the original poster asked about, namely $$\vec{n}\times(\vec{H_2} - \vec{H_1})=\vec{K} .$$

Which part you don't get that the OP was asking about the tangential H field and current in question 3? That EM wave produce current by boundary condition?
Read Field and Wave Electromagnetics by David K Cheng page 262 that clearly state the tangential H field create surface current. AND page 331 to 332 CLEARLY explains FREE current density created at the boundary between dielectric and good conductor in equation 7-70.

$$\hat A_{n2}\;\times\;(\vec H_1-\vec H_2)= \vec J_s$$
Then in page 430 and 431. It explain the boundary condition creates SURFACE CURRENT on the conductor plates of the parallel plate tx line.
$$\hat a_y \;\times\; \vec H=\vec J_{su}\;$$

See the attached image of p430 below. If you don't think the boundary condition produce surface current, why are you saying K in your equation is surface current? Your equation is almost exactly the same as I quoted from the book. Are you confused?

AND in Engineering Electromagnetic page 182:

https://www.amazon.com/Electromagnetics-Engineers-Fawwaz-T-Ulaby/dp/0131497243/ref=sr_1_1?s=books&ie=UTF8&qid=1356415210&sr=1-1&keywords=engineering+electromagnetics+ulaby

$$\int_s(\nabla \times \vec H)\cdot d\vec s =\int_s \vec J\cdot d\vec s \;+\; \int_s\frac{\partial \vec D}{\partial t}\cdot d\vec s = I_c+I_D$$
Where Ic is CONDUCTIVE current and Id is DISPLACEMENT current.

Then refer to Introduction to electrodynamics by David Griffiths P332. It explains discontinued tangential H across the boundary produces FREE surface current density.

https://www.amazon.com/Introduction-Electrodynamics-3rd-David-Griffiths/dp/013805326X/ref=sr_1_1?s=books&ie=UTF8&qid=1356428777&sr=1-1&keywords=introduction+to+electrodynamics

This one, you can actually read the content of the book. Go to page 332.

This is CLEARLY STATED in the book. In the boundary condition, it is the SURFACE CONDUCTION CURRENT.

3) Conduction does not occur by electrons jumping from one atom to the next.
As I said, you can look at it as it's a cloud of conductive band or the atom share the valency electrons, they move around, and they can drop back to the atom depend on the energy. That's is electron move from one to the other in my book.

4) Current (or conduction) is always spoken of as being driven ultimately by potential energy differences. Hence current in a charge-neutral wire is the gradient of a potential, leading to Ohm’s law being written $$\vec{J}=\sigma \vec{E}$$ rather than the other way around. Furthermore, we always measure "I-V" curves where V is the independent variable. As a result, drift velocity increases in copper samples of greater purity and decreases in dirtier samples.
I response to this already in post #12.
5) Post 6 gives a rather roundabout argument that a time-invariant form of Kirchoff’s laws cannot be applied to a time varying circuit. This, of course, merely restates the condition that gave rise to the original question. The answer to the question is to form Kirchoff’s laws to include the time-varying terms in Maxwell’s equations. Including dB/dt introduces into the circuit some emf’s due to self and mutual induction, as the_emi_guy has already pointed out. Including dD/dt allows the treatment of displacement currents in capacitors.
You better argue with Professor Lavine of MIT. I can see his arguement that the electric field under varying magnetic field is not conservative.
6) “Electromagnetic is the most difficult subject in EE by a mile.” There are topics (stability of a system, information capacity of a multipath scattering communication channel, maximum entropy spectral analysis, error correction coding, etc.) that others could claim are much more difficult than the problems we are dealing with here.
That's is an opinion, You have yours and I have mine.

yungman, I have asked you in previous threads not to post erroneous answers in areas where you are not an expert. You state here, instead, that you post what you like and want other people to correct you, and that you like to argue with the corrections. This is counterproductive from many standpoints. I'll give three:
1. It is tedious for those (myself in this case, others in previous threads of yours) whom you expect to a) wade through your voluminous posts, b) try to correct your errors and misconceptions, and c) then argue with you.
2. You spread confusion and misinformation. In this case, you confused the original poster CheyenneXia, at the very least.
3. You undermine your own credibility, and also make it less likely that experts will be interested in engaging with you.

I believe restraint is the better approach.

You make the accusation, it's up to you to make the correction. You are the adviser and you make the statement. So it is your responsibility to correct any inaccuracy here.

Condescending comments have no place in this forum. If you don't agree, state the reason.

Attached is an image of page 430. It is blur as I have to shrink the size to 300K. The equation in question is 9-7b for the upper plate. Ignore all my hand written notes, just read the text of the book. The second image is my drawing according to the figure from the book, I added color and more detail. The figure at the bottom of the text page is Fig.9-3 if you care to read the text.

$$-\hat a_y\times \vec H=\vec J_{su}$$

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Also I'll point out that you have completely hijacked this thread so it is focused on a topic taken from your own, different thread.

You read the original question? Question 1 is on KVL under magnetic field condition. Question 3 about tangential boundary condition which talk about free charge and free current. Where is it off the topics when I talk about MIT professor Levine. He made a video demonstrated KVL don't hold under varying magnetic field. AND current in transmission line are consequence of EXACTLY the tangential boundary condition between good conductor and dielectric. You watch the video I posted before you speak?

Locked pending moderation.

berkeman
Mentor
This thread will remain closed. I've asked yungman to take the debate to PMs if he wants to continue it.