Question

a non conducting hemisphere of dielectric constant Unity has uniform volume charge density rho if minus Q charge flights from its flat surface to infinity find the work done for the same​

Answer 1

considered a shell of radius X and thickness dX in the form of hemisphere

then volume of shell =2πx^2dx

electric charge on the shell

dQ=(2πx^2dx)p

P.E.due to shell ,dU=1/4π£ (-q)dQ/x

=-ap/2£ xdx

since at infinity ,U=0,so

total work done =qpR^2/4£

Answer 2

at initial u is equal to 0

so total work done is qpr/4£