If the electrostatic potential v 5 v at r2nbsp mnbsp find

Question

Question:

Given an electric field in spherical coordinates given by
E=  A r â_r V/m   for r<1 m

E=0                     for r>=1 m

(a) If the electrostatic potential V = 5 V at r=2  m,  find the electrostatic potential V at r = 0

(b) Find the volume charge density ρ_v for all r.

(c) The electric field drops abruptly to zero at r= 1 m. This tells us that a surface charge exists on the spherical surface at radius r = 1 m.

Find the surface charge density ρ_s      .

Hint: Gauss's Law is helpful here.