$3).$

A rectangular conducting plate lies in the xy plane, occupying the region $0<$ x $<$ a$,0<$ y $<$ b$.$ An identical conducting plate is filled with material having conductivity sigma$($x$)=$ sigma$0$e$^-$x$/$a $,$ where sigma$0$ is a constant. Voltage V$0$ is applied to the plate at z $=$ d; the plate at z $=0$ is at zero potential. Find, in terms of the given parameters:

a$)$ The electric field intensity E within the material

b$)$ the total current flowing between plates

c$)$ the resistance of the material