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 outer sphere is earthed and when inner sphere is earthed will be
Diffcult
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(c) Capacity when outer sphere is earthed
${C_1} = 4\pi {\varepsilon _0}\frac{{ab}}{{b - a}}$
Capacity when inner sphere is earthed
${C_2} = 4\pi {\varepsilon _0}b + \frac{{4\pi {\varepsilon _0}ab}}{{b - a}} = 4\pi {\varepsilon _0}\left( {\frac{{{b^2}}}{{b - a}}} \right)$
Difference in capacity = $C_2 -C_1 = 4\pi {\varepsilon _0}b$
${C_1} = 4\pi {\varepsilon _0}\frac{{ab}}{{b - a}}$
Capacity when inner sphere is earthed
${C_2} = 4\pi {\varepsilon _0}b + \frac{{4\pi {\varepsilon _0}ab}}{{b - a}} = 4\pi {\varepsilon _0}\left( {\frac{{{b^2}}}{{b - a}}} \right)$
Difference in capacity = $C_2 -C_1 = 4\pi {\varepsilon _0}b$
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