$(50)$ An electric potential is given by V $($x$,$ y$)=$ c cos$($x$)$ sin$($y$),$ where c is a constant

and x and y are coordinates. It is known that the electric field can be computed from

E $=$V $.($a$)$ Find E $=$V $($x$,$ y$).($b$)$ What is the maximum value $($amplitude$)$ of

E$?($c$)$ The charge density $($x$,$ y$)=0$ E$.$ Find and compare it with the potential

and what you find.