Chapter 14.5, Problem 63E

Ampere’s Law One of Maxwell’s equations for electromagnetic waves is $\nabla \times B=C\frac{\partial E}{\partial t}$, where E is the electric field, B is the magnetic field, and C is a constant.

a.    Show that the fields $E\left(z,t\right)=A\sin \left(kz-\omega t\right)iB\left(z,t\right)=A\sin \left(kz-\omega t\right)j$ satisfy the equation for constants A. k, and ω, provided $\omega =k/C$.

b.    Make a rough sketch showing the directions of E and B