PHYSICS 306
Problem Set: 5
Due Date: 17.5.18
Consider the plane monochromatic plane waves propagating along z-axis, so E and B are given by;
$\mathbf{E}(x, y, z, t) = \mathbf{E}(x, y)e^{i(kz - \omega t)}$,
$\mathbf{B}(x, y, z, t) = \mathbf{B}(x, y)e^{i(kz - \omega t)}$
Use Maxwell's equations to show that $\mathbf{E}_x$ and $\mathbf{B}_x$ satisfies the following equations.
$(
\frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} + (\omega/c)^2 - k^2)\mathbf{E}_x = 0$,
$(
\frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} + (\omega/c)^2 - k^2)\mathbf{B}_x = 0$.
