Question

Finding amplitude of magnetic field from electric field

Answer 1

Answer:

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Answer 2

Answer:

We have

By=B0+B0sin(kx+ωt)=B0+B0cos(π2−kx−ωt)=B0+B0Re[ej(π2−kx−ωt)]

hence, k⃗ =(k,0,0)⇒k^=(1,0,0).

Now, my problem is with part 2. I tried to use Maxwell equations ∇×B=μ0J+1c2∂E∂t and ∇×E=−∂B∂t. In the first equation, I don't J and in the second one, I don't know how to solve for E.

Part 3 is simple after solving part 2.

How should one solve part 2? any help would be appreciated.