Sphere in the figure is a spherical capacitor with inner sphere earthed. The capacitance of the system is
Answer & explanation
Correct answer: option 2
The potential on the outer sphere is V (let). Thus we can consider two capacitors between the outer sphere and inner sphere C1 and outer sphere and earth C2. These two capacitors are in parallel.
Thus, $C_1=4 \pi \varepsilon_0 \frac{ab}{b-a}$
$C_2=4 \pi \varepsilon_0 b$
$C_1=4 \pi \varepsilon_0 \frac{ab}{b-a}+4 \pi \varepsilon_0 b$
$\Rightarrow C=\frac{4 \pi \varepsilon_0 b^2}{b-a}$
∴ (B) is correct.