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Question

(A) Let the inner radius be $r = 2 	ext{ cm}$ and the outer radius be $R = 5 	ext{ cm}$.When the outer sphere is earthed,the capacitance is given by

Vedclass · Accepted Answer

$\frac{5}{2}$

Vedclass · Answer

(A) Let the inner radius be $r = 2 	ext{ cm}$ and the outer radius be $R = 5 	ext{ cm}$.When the outer sphere is earthed,the capacitance is given by $C_2 = 4 \pi \varepsilon_0 \frac{rR}{R-r}$.Substituting the values: $C_2 = 4 \pi \varepsilon_0 \frac{2 	imes 5}{5-2} = 4 \pi \varepsilon_0 \frac{10}{3}$.When the inner sphere is earthed,the capacitance $C_1$ is the sum of the capacitance of the spherical capacitor and the capacitance of the outer sphere alone (as the outer sphere is now at potential $V$ and the inner is at $0$): $C_1 = 4 \pi \varepsilon_0 \frac{rR}{R-r} + 4 \pi \varepsilon_0 R$.Substituting the values: $C_1 = 4 \pi \varepsilon_0 \left( \frac{10}{3} + 5 ight) = 4 \pi \varepsilon_0 \left( \frac{10+15}{3} ight) = 4 \pi \varepsilon_0 \frac{25}{3}$.Now,the ratio $\frac{C_1}{C_2} = \frac{4 \pi \varepsilon_0 (25/3)}{4 \pi \varepsilon_0 (10/3)} = \frac{25}{10} = \frac{5}{2}$.Thus,the correct option is $A$.

$A$ spherical capacitor has an outer sphere of radius $5 \text{ cm}$ and an inner sphere of radius $2 \text{ cm}$. When the inner sphere is earthed,its capacity is $C_1$,and when the outer sphere is earthed,its capacity is $C_2$. Then $\frac{C_1}{C_2}$ is

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