Question

A spherical shell of radius \(R\) has charge \(Q\) uniformly distributed over its surface. The work done in this process is:

• A. \(\frac{Q^2}{4\pi \varepsilon_0 R}\)
• B. \(\frac{Q^2}{8\pi \varepsilon_0 R}\)
• C. \(\frac{Q^2}{16\pi \varepsilon_0 R}\)
• D. \(\frac{Q^2}{32\pi \varepsilon_0 R}\)

Hint:

Electrostatic energy of a charged spherical shell is always \(W = \frac{1}{2}QV\).

Answer 1

The Correct Option is B

Step 1: Electrostatic energy concept.
The work equals the stored potential energy of the charge distribution.

Step 2: Potential of a spherical shell.
V = (1/4πε₀)(Q/R).

Step 3: Work expression.
W = ½ Q V.

Step 4: Substituting V.
W = ½ Q × (1/4πε₀)(Q/R).

Step 5: Simplifying.
W = Q²/(8πε₀ R).

Step 6: Conclusion.
The work done is Q²/(8πε₀ R).