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Q.

Assume three concentric, conducting spheres where charge q₁ and q₂ have been placed on inner and outer sphere where as middle sphere has been earthed. Find the charge on the outer surface of middle spherical conductor

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a

$\frac{b}{c} q_{1}$

b

– q₁

c

$- \frac{b}{c} q_{2}$

d

– q₂

answer is A.

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Detailed Solution

-q₁ charge on inner and + q on outer surface are induced on middle sphere. Then
$\begin{array}{l} V_{net} = \frac{1}{4 {πε}_{0}} [\frac{q_{1}}{b} + \frac{q - q_{1}}{b} + \frac{q_{2}}{c}] = 0 \\ \frac{q}{b} + \frac{q_{2}}{c} = 0; q = - \frac{b}{c} q_{2} \end{array}$

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