# EM plane wave incident upon infinite sheet of current

1. Mar 16, 2013

### aftershock

1. The problem statement, all variables and given/known data

What are the electric and magnetic fields due to an infinite sheet of surface current $\vec{K}$ = $\hat{j}$Ko in the plane x=0? The plane is electrically neutral and Ko is a constant. Plane electromagnetic waves are APPROACHING the plane x =0 from either side, incident normally with the magnetic field given by -$\hat{k}$Bocos(kx+ωt) for x>0 and $\hat{k}$Bocos(kx-ωt) for x<0

Find the electric field $\vec{E}$($\vec{r}$,t) on either side of the plane x=0

Find the current (surface current) in the plane x=0?

2. Relevant equations

3. The attempt at a solution

There is no electric field caused by the plane since it is electrically neutral. Using ampere's law I determined the magnetic field to be 2μk$\hat{z}$ (negative on the positive side of the plane).

To find the electric field on both sides I'm assuming I just consider the electric field of the EM wave and use the E/c = B relation. This is easy enough so far but then it asks me to find the surface current in the plane. The surface current is given in the problem, so I'm assuming the waves affect the surface current to give me a new value? Is this correct, and if so how do I go about it?