Question

Find magnetic field from electric field funciton

Answer 1

Hold your right hand flat in front of your face with your thumb stuck out on the side at a right angle in the shape of an "L". Now rotate your hand until your fingers point in the direction of the electric field and your palm faces in the direction of the magnetic field

Answer 2

Answer:

here is your 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.

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