Good day to everyone!

Please, I am in search of a book that describe how derive Kirchhoff's
Current Law (KCL), Kirchhoff's Voltage Law (KVL), Ohm's law from
Maxwell's equations.

I have seen something using the Perturbation theory (quantum
mechanics) and I know that something has been written in
Electromagnetic Fields, Energy, and Forces by Robert M. With Lan Jen
Chu and Richard B. Adler Fano.

have you other suggestion?

thank you and sorry for my "school of broken english"

G.M.S.
Italy

Good day to everyone!

Please, I am in search of a book that describe how derive Kirchhoff's
Current Law (KCL), Kirchhoff's Voltage Law (KVL), Ohm's law from
Maxwell's equations.

I have seen something using the Perturbation theory (quantum
mechanics) and I know that something has been written in
Electromagnetic Fields, Energy, and Forces by Robert M. With Lan Jen
Chu and Richard B. Adler Fano.

You're not going to get Ohm's law from the Maxwell equations. The
minimal set would be the Lorentz force law, and diffusion subject to an
external force. This will give you Ohm's law qualitatively, but isn't
going to tell you the conductivity of any real material (you might get
this in a heavy-duty solid state physics book). Easy enough - in the
diffusive regime, the electron drift velocity is proportional to the
electric field, this velocity and the electron density tell you the
current. The voltage drop is just V=E*L, where L is the length of the
conductor.

For the voltage law, you just need the fact that you can express the
electrostatic field as the gradient of a scalar potential (which you can
show from the Maxwell equations if you wish). Integrate E.dl about a
closed loop and what answer do you get?

For the current law, just use conservation of charge, which, again, you
can show from the Maxwell equations.

Of the three laws you're asking about, Ohm's law is the only difficult
one, and it's very difficult, especially if you want to deal with real
materials, for which the conductivity is not a constant. Ohm's law is a
convenient approximation, very useful since it's simple, but it isn't
correct in a strict sense. It's usually just assumed as one of the three
constitutive relations in classical electromagnetism (J=conductivity*E,
along with D=epsilon*E, B=mu*H).

Thanks Timo, but i know what you are saying.
I need the complete bound between Maxwell's low and KVL and KCL for a
formal demostration in Electromagnetic Compatibility course at
University (Politecnico Tourin - Electronic engineering).
With the perturbation theory (http://en.wikipedia.org/wiki/
Perturbation_theory), working on parameter i can made a bound with
dimensional and "tipical" timing of a circuit, defining a break point
where classic kvl and kcl don't give exact solvutions.
A0 order give us classic kvl and kcl
The "higher orders" rapresent for ex. (depends on witch maxwell's
equation you are working on) external magnetic influence.

We have done a "first" demostration of this in classroom, and
something about it is written in
Electromagnetic Fields, Energy, and Forces by Robert M. With Lan Jen
Chu and Richard B. Adler Fano (year 1960, little problem to found
it!).

Not a lot about it has been written, some scientific articles... so i
was in search of some news on this specific application for write a
little "thesis" (not the final one of my study )

Well then, you need to consider when the static/quasi-static assumptions
fail. When does radiation become important? Is there any other
electromagnetic effect other than radiation that can make circuit theory
fail? Why or why not? There was a paper addressing some of this in the
last few months on this in Am. J. Phys., iirc, and there have been other
related papers in the past in the same journal.

As it's for assessment, the point is to show what you know and
_understand_, rather than what other people know (at least, it should be
the point!). For example, why do you choose a particular break point where
the circuit laws fail? What does this break point mean physically, beyond
being a usual engineering rule-of-thumb?

KVL is about how well a voltage (does this depend on gauge?) behaves as
you become non-electrostatic. KCL depends on how well you can talk about
"current in a wire", with non-static fields. How do you decide where to
choose a break-point?

--
Timo Nieminen - Home page:http://www.physics.uq.edu.au/people/nieminen/
E-prints:http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits:http://www.users.bigpond.com/timo_nieminen/spirits.html

Hi Timo,

My gratitude debt with you is every-day greater! :-D

You are right in all exept one thing. The assessment :-D

I'am 30, i can not study when it was time and i am studying now with
huge effort
1- because i have lost a lot of physics grounds
2- because i have to share my time with family and work
So, now, assessment in not the real target of my study, i study
because i WANT

My need of know what other people know is because the objective of my
essay is a
comparison of the ways used to define a break point that i tnink is
allready well know:
- the circuit laws start to fail when circuit's size are of same order
of magnitude of wavelength of signals we are using
Far from this condition we use circuits low. Under this condition we
have Microwave Engineering.

Sure, circuit theory and it's limitations ARE well known!
[...]
The problem is that everyday many people use circuit theory and field
theory but have pretty much forgotten how one is an approximation of
the other and the conditions necessary for that approximation to hold.

I am really sorry Benj, but i think i have problems to explain my
point :-(

There is a brackpoint, you have defined circuit's low, but htere is
more...
Perturbation theory IS my point because give approximate solution to
maxwell's equation and at the
0 order i can find the "classical" explanation about integration about
a loop in a CONSERVATIVE field gives zero, ecc..
but at the highest order i find important solution in EMC study....
that is what i am searching...

sorry, i do not know the right way to explain myself
it sound me like i ask you about pinapple and you asware me about
apple ((

I think that FIRST, before UNDERSTAND, is better impruve english :-P

GMS

On 11 Ott, 20:27, Benj <bjac...@iwaynet.net> wrote:

Sure, circuit theory and it's limitations ARE well known!
[...]
The problem is that everyday many people use circuit theory and field
theory but have pretty much forgotten how one is an approximation of
the other and the conditions necessary for that approximation to hold.
-----------