Question

A metal ball of radius R is placed concentrically
inside a hollow metal sphere of inner radius 2R and
outer radius 3R. The ball is given a charge +2Q and
the hollow sphere a total charge –Q. The
electrostatic potential energy of this system is

Answer 1

The electrostatic potential energy of this system is U = 10σQR /3ε0.

Explanation:

• The metal ball of radius R is having charge +2Q and a hollow sphere of inner and outer radius 2R and 3R is given charge −Q.
• By induction ,inner wall of hollow sphere is induced with charge −2Q and its outer surface with charge +2Q.

Net charge on outer surface of hollow sphere = +2Q−Q = +Q.+Q

= σ × 4π(9R^2 − 4R^2)

= 20πσR^2.

The potential at the outer surface of hollow sphere.

V = 1/4πε0 ×+Q/3R

= 1/4πε0×+20πσR^2 / 3R.

The potential energy due to system of charges +2Q and +Q is given by.

U = +2Q×V = +2Q× (1/4πε0 × +20πσR^2 / 3R)

U = 1/4πε0 × +2Q × 20πσR^2 / 3R

U = 1/4πε0 × 40πσQR/3 = 10σQR /3ε0.

Thus the electrostatic potential energy of this system is U = 10σQR /3ε0.

Also learn more

Two charges of magnitudes 5nC and -2nC are placed at points (2cm,0,0) and (x,0,0) in a region of free space where there is no other external field .If the electrostatic potential energy of whole system is -0.5 mJ .What is the value of x ?

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