Question

Two conducting shells of radius a and b are connected by a conducting wire as shown in figure. The capacity of system is: 

• A. 4πvarepsilon₀ (ab)/(b-a)
• B. 4πvarepsilon₀ (a+b)
• C. zero
• D. infinite

Hint:

If the outer spherical shell is grounded, the system behaves exactly like a spherical capacitor.

Answer 1

The Correct Option is A

Step 1: Since the two shells are connected by a wire, they are at the same potential.

Step 2: The outer shell is grounded, so the system behaves like a spherical capacitor with: inner radius = a, outer radius = b 

Step 3: Capacitance of a spherical capacitor: C = 4πvarepsilon₀ (ab)/(b-a)