Chapter 13.1, Problem 3P

Assume from electrodynamics the following equations which are valid in free space. (They are called Maxwell’s equations.) $\nabla \cdot E=0\nabla \cdot B=0$ $\nabla \times E=-\frac{\partial B}{\partial t}\nabla \times B=\frac{1}{c^2}\frac{\partial E}{\partial t}$ where $E$ and $B$ are the electric and magnetic fields, and $c$ is the speed of light in a vacuum. From them show that any component of E or $B$ satisfies the wave equation (1.4) with $v=c.$