Question

A solid spherical non conductor of radius 5 cm has potential of 50 V on its outer surface. The potential at its centre is

Answer 1

potential at r distance from the centrre of a non conducting solid sphere of radius R  is given by 
     V(r) = KQ/2R (3 - r²/R²)

so, potential at outer surface is given by,
                                         V(R) = KQ/2R(3 - R²/R²)
                                                 = KQ/2R × 2 
                                                 = KQ/R 
given, potential at outer surface of sphere ,V(R) = 50V
radius of sphere , R = 5cm = 0.05 m
 ⇒ 50 = KQ/0.05 
⇒ KQ = 2.5 -----------------(1)

      now, potential at centre of the surfce is given by,
 V(r = 0) = KQ/2R(3 - 0/R²)
              = 3KQ/2R 
from equation (1),
   V(r = 0) = 3 × 2.5/2 × 0.05 = 75V

hence, potential at its centre is 75v