Question

HELP, I need help understanding the solution to this problem.

Answer 1

I just don't understand how you use the RHR to find the direction of B if you're only given the direction of E?

Answer 2

FWIW i see what you mean

i thought you found B, given E, from the 3rd Maxwell Equation

so for the E wave you have, you can say \(\nabla \times \vec E = k E_o \sin (kx - \omega t ) ~ \hat k = - \dfrac{\partial \vec B}{\partial t}\)

maybe there's another way of replacing that with just pointing your fingers the right way, but i don't know it i'm afraid