sci.physics.electromag

On Tue, 9 Oct 2007, @ wrote:

> 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 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).

--
Timo Nieminen - Home page: /people/nieminen/
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