Consider three concentric metallic spheres A, | vedclass

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Question

(A) Since spheres $A$ and $B$ are connected,they act as a single conductor at the same potential. Let the charge on the combined system $(A+B)$ be $q$

Vedclass · Accepted Answer

$-4 \pi \varepsilon_0 V \frac{b c}{c-b}$

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(A) Since spheres $A$ and $B$ are connected,they act as a single conductor at the same potential. Let the charge on the combined system $(A+B)$ be $q$ and the charge on sphere $C$ be $Q_C$.The potential of the system $(A+B)$ is given by:$V_B = \frac{1}{4 \pi \varepsilon_0} \left( \frac{q}{b} + \frac{Q_C}{c} \right) = V$Since sphere $C$ is grounded,its potential is zero:$V_C = \frac{1}{4 \pi \varepsilon_0} \left( \frac{q}{c} + \frac{Q_C}{c} \right) = 0$From the second equation,we get $q + Q_C = 0$,which implies $q = -Q_C$.Substituting $q = -Q_C$ into the first equation:$V = \frac{1}{4 \pi \varepsilon_0} \left( \frac{-Q_C}{b} + \frac{Q_C}{c} \right)$$V = \frac{Q_C}{4 \pi \varepsilon_0} \left( \frac{1}{c} - \frac{1}{b} \right) = \frac{Q_C}{4 \pi \varepsilon_0} \left( \frac{b-c}{bc} \right)$Solving for $Q_C$:$Q_C = 4 \pi \varepsilon_0 V \left( \frac{bc}{b-c} \right) = -4 \pi \varepsilon_0 V \left( \frac{bc}{c-b} \right)$

Consider three concentric metallic spheres $A, B$ and $C$ of radii $a, b, c$ respectively,where $a < b < c$. $A$ and $B$ are connected,whereas $C$ is grounded. The potential of the middle sphere $B$ is raised to $V$. Then the charge on the sphere $C$ is

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