Question

A solid conducting sphere, having a charge Q, is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given a charge of –4 Q, the new potential difference between the same two surface is:
(A) 2 V (B) –2V
(C) 4 V (D) V

Answer 1

Answer:

a or b

Explanation:

probably b. .......

Answer 2

The new potential difference between the 2 surfaces is:

(D) V

This can be found as follows:

• As per the question, Initially,

       Vi−Vo = (kQ/r₁) − (​kQ/r₂​)

                  = kQ (1/r₁ - 1/r₂​)

                  = V

• Now, When –4 Q charge is given to the shell, then,

        Vi−Vo = (kQ/r₁) − (4​kQ/r₁​) -  (kQ/r₂) − (​4kQ/r₂​)

                   = kQ/r₁ - kQ/r₂​

                   = kQ (1/r₁ - 1/r₂​)

                   = V

• In both cases, the potential difference doesn't change. It remains V.

• Therefore, the new potential difference is V.