Question

Finding magnetic field from electric field example

Answer 1

Let B=(0,B0[1+sin(kx+ωt)],0)B=(0,B0[1+sin⁡(kx+ωt)],0) be the magnetic field of some electromagnetic plane wave.

Find the wave direction vector.

Find the electric field.

Compute the Poynting vector and the energy density.

Part 11:

We have

By=B0+B0sin(kx+ωt)=B0+B0cos(π2−kx−ωt)=B0+B0Re[ej(π2−kx−ωt)]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)k→=(k,0,0)⇒k^=(1,0,0).

Now, my problem is with part 22. I tried to use Maxwell equations ∇×B=μ0J+1c2

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.

mark me brainiest