Question

The figure shows a spherical capacitor with inner sphere earthed. The capacitance of the system is

• A. $\frac { 4 \pi \varepsilon _ { 0 } a b } { b - a }$
• B. $\frac { 4 \pi \varepsilon _ { 0 } b ^ { 2 } } { b - a }$
• C. 4 πε₀ (b + a)
• D. None of these

Answer 1

Answer: (B)

$\frac { 4 \pi \varepsilon _ { 0 } b ^ { 2 } } { b - a }$

Answer 2

Let V be potential on the outer sphere. Thus we can consider two capacitors between the outer sphere and inner sphere (1) and outer sphere and earth

Thus, C₁ = 4π ε₀ $\frac { a b } { b - a }$ ; C₂ = 4π ε₀ b

C =4πε₀ $\frac { a b } { b - a }$ + 4π ε₀ b ⇒ C =