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(C) Let the charge on the inner sphere be $q$ and the charge on the outer sphere be $Q$. For any point $P$ at a distance $x$ from the center,where $x

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$-Q$

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(C) Let the charge on the inner sphere be $q$ and the charge on the outer sphere be $Q$. For any point $P$ at a distance $x$ from the center,where $x > R$,both spheres act as point charges located at the center. The electric potential $V$ at point $P$ is given by the sum of the potentials due to both spheres: $V = \frac{1}{4 \pi \epsilon_0} \frac{q}{x} + \frac{1}{4 \pi \epsilon_0} \frac{Q}{x}$ We are given that the potential at point $P$ is zero,so: $V = \frac{1}{4 \pi \epsilon_0 x} (q + Q) = 0$ Since $\frac{1}{4 \pi \epsilon_0 x} 
eq 0$,we must have: $q + Q = 0$ $q = -Q$ Thus,the charge that should be given to the inner sphere is $-Q$.

Two concentric hollow conducting spheres of radius $r$ and $R$ $(r < R)$ are shown. The charge on the outer shell is $Q$. What charge $q$ should be given to the inner sphere so that the potential at any point $P$ at a distance $x$ $(x > R)$ from the center is zero?

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