An infinitely thin flat sheet of charge with density per unit area $$ occupies the $xy$ plane. The

charges are forced to oscillate along the hat$(x)$ direction so that their velocity at time $t$ is vec$(v)=$

hat$(x)v_{0}cos(t),$ resulting in electromagnetic radiation.

a$)$ Solve for the magnetic and electric fields everywhere as a function of time. $[25$ points$]$

b$)$ How much energy per unit area is radiated away in a long time $T?[15$ points$]$