A spherical condenser has inner and outer sph | vedclass

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(C) When the outer sphere is earthed,the capacitance $C_1$ of the spherical capacitor is given by: $C_1 = 4\pi \varepsilon_0 \frac{ab}{b - a}$ When th

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$4\pi \varepsilon_0 b$

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(C) When the outer sphere is earthed,the capacitance $C_1$ of the spherical capacitor is given by: $C_1 = 4\pi \varepsilon_0 \frac{ab}{b - a}$ When the inner sphere is earthed,the outer sphere acts as an isolated conductor with capacitance $4\pi \varepsilon_0 b$ in parallel with the spherical capacitor. Thus,the total capacitance $C_2$ is: $C_2 = 4\pi \varepsilon_0 b + \frac{4\pi \varepsilon_0 ab}{b - a} = 4\pi \varepsilon_0 \left( \frac{b(b - a) + ab}{b - a} \right) = 4\pi \varepsilon_0 \left( \frac{b^2 - ab + ab}{b - a} \right) = 4\pi \varepsilon_0 \frac{b^2}{b - a}$ The difference in capacities is: $C_2 - C_1 = 4\pi \varepsilon_0 \left( \frac{b^2}{b - a} - \frac{ab}{b - a} \right) = 4\pi \varepsilon_0 \left( \frac{b^2 - ab}{b - a} \right) = 4\pi \varepsilon_0 \frac{b(b - a)}{b - a} = 4\pi \varepsilon_0 b$

$A$ spherical condenser has inner and outer spheres of radii $a$ and $b$ respectively. The space between the two is filled with air. The difference between the capacities of two condensers formed when the outer sphere is earthed and when the inner sphere is earthed will be:

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