$4$: Verify that E$($x$,$ t$)=$ Emax sin$($kx $$ t$)$ satisfies the wave equation

$2$E

$$t$2=1$

$0$$0$

$2$E

$$x$2$

when

k $=$ c $=1$$0$$0.$

$5$a: The magnetic field of an electromagnetic wave is described by

$$

B$($z$,$ t$)=106$ sin$(105$z $$ t$)($x$)$ T

Determine the electric field completely.