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A system consists of two conducting concentric spheres, with the inner sphere of radius ‘a’ carrying a positive charge q. What charge q has to be deposited on the outer sphere of radius ‘b’ to reduce the potential of the inner sphere to zero?

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Potential of the inner sphere of charge Q is due to its own charge and due to the charge q on the outer sphere.
Potential due to charge Q at the inner surface =$\large\frac{Q}{4 \pi \in_0 a}$
Potential due to charge q (present on the outer sphere) at the inner sphere $= \large\frac{q}{4 \pi \in_0 b}$
Net potential on the inner sphere $=\bigg( \large\frac{Q}{4 \pi \in_0 a} +\frac{q}{4 \pi \in_0 b}\bigg)$
To make the net potential zero
$=\bigg( \large\frac{Q}{4 \pi \in_0 a} +\frac{q}{4 \pi \in_0 b}\bigg)$$=0$
$=> q=-Q \large\frac{b}{a}$
answered Jun 7, 2014 by meena.p
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