Two spherical conductors $A$ and $B$ of radii $a$ and $b$ $(ba)$ are placed concentrically in air. The two are connected by a copper wire as shown in figure. Then the equivalent capacitance of the system is

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Two spherical conductors $A$ and $B$ of radii $a$ and $b$ $(b>a)$ are placed concentrically in air. The two are connected by a copper wire as shown in figure. Then the equivalent capacitance of the system is

Aicharya · Accepted Answer

For a while, let's assume that there is no connection between the inner and outer spheres. The two spheres on given some charges $\mathrm{q}_1 ~\&~ \mathrm{q}_2$. Now, $v_a=\frac{k q_1}{a}+\frac{k q_2}{b}$ $v_b=\frac{k q_1}{b}+\frac{k q_2}{b}$ So, $\mathrm{V}_{\mathrm{a}}>\mathrm{V}_{\mathrm{b}}$ This directly implies that any charges given to inner sphere will move to the outer sphere if the two are provided with a connection. Therefore, the setup is equivalent to an isolated spherical conductor of radius b. And we know for such a case $C=4 \pi \epsilon_0 R=4 \pi \epsilon_0 b$ ~

Two spherical conductors $A$ and $B$ of radii $a$ and $b$ $(b>a)$ are placed concentrically in air. The two…

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