Question

Corresponding magnetic field of given electric field

Answer 1

Given the following electric field: E⃗ (r,t)=Re{[Eox^+iEoy^]exp[ 2πi ((2⋅104cm−1) z − (5⋅1014s−1) t)]}

I wish to find an expression for the magnetic field in a medium of refractive index n>1. What I know so far:

∇⃗ ⋅B⃗ =0∇⃗ ×B⃗ =ϵμ∂E⃗ ∂t+μJ⃗

Because J⃗ =0 and charge density is 0 (electromagnetic wave), this will be E⃗ =B⃗ ×v⃗ . However, I'm drawing a blank on how to finish solving the problem. Can anybody point me in the right direction?

EDIT: Forgot to mention that μr=1.