EM field due to a long wire submitted to an AC current

[jfgobin]

Hello there,

I am having a real stupid moment.

In the space XYZ, a long wire is along the Y axis and is submitted to an alternating current I_{0}\sin \omega t. I am trying to establish the equations for the B(t) and E(t) fields along the X axis.

I assume that the distance to the cable is small in regard to the cable length and that the cable length is small in regard to the wavelength of the alternating signal, so the cable can be seen as having a uniform current along its length. I am pretty sure the problem will have a cylindrical symmetry.

Besides the "use Maxwell's equations", any hint to attack this problem?

Thanks to all!

 

[mfb]

"use retarded potentials"?

If the distance to the cable is small compared to the wavelength of the alternating signal (if not, the finite cable length is a problem!), you can neglect the time-dependence of the current to get a good approximation.