Adding a Phase Element to Biot Savart Law

[lechko]

Hi everyone, just got something new to do and got no idea where to start.
I'm trying to add a phase element to Biot Savart law (thus turning it from a static law to something that will apply to various freq.) to do that, I'm reading up on how the law was proved.
As far as i can understand, it all started from Laplace, using the magnetic potential function, you get the equation for magnetic field and so on... the question is how do i add the phase element in? is it as simple as multiplying J (current flux) by { exp(-jkr) } and going on with it to getting same as Biot Savart but with the added part?

I'm out of ideas here, so any help will be great.

 

[Gza]

Biot-Savart is an experimental law (But I think there's a derivation of it from maxwell's equations and relativity in the book "Principles of Electrodynamics" by Melvin Schwartz.) When you say static, I assume you mean magneostatic, since the law applies in the presence of a non-static electric field (which is manifested as a magnetic field without taking Lorentz into account.) I'm still not too clear what you are trying to do with it, but whenever you have a changing magnetic field, you will have to take into account Faraday's Law somehow.

 

[pervect]

Hi everyone, just got something new to do and got no idea where to start.
I'm trying to add a phase element to Biot Savart law (thus turning it from a static law to something that will apply to various freq.)
I'm out of ideas here, so any help will be great.

I'm not sure of the details of what you're trying to do, but it seems to me that all you really want to do is to take the Fourier or laplace transform to take the problem out of the time domain into the frequency domain.