Three identical metal plates with large surface areas are kept parallel to each other as shown in figure. The left most plates is given a charge $Q$ and the right most plate $C$ is given a charge $-2Q.$ The middle plate $B$ is neutral. Then the charge appearing on the outer surface $S$ of the plate $C$ is :-
Medium
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The net field inside plate $\mathrm{C}$ at say point $\mathrm{P}$ should be zero. Let $\mathrm{q}$ is charge on $\mathrm{S}.$ Then field at $\mathrm{P}$ from all the charges (plate $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ ) is
$\frac{{{\rm{Q}}/2{\rm{A}}}}{{{ \in _0}}} + 0 - \frac{{(2{\rm{Q}} + {\rm{q}})/{\rm{A}}}}{{2{ \in _0}}} - \frac{{{\rm{q}}/{\rm{A}}}}{{2{ \in _0}}} = 0$
or $\mathrm{Q}-2 \mathrm{Q}-\mathrm{q}-\mathrm{q}=0$
or $\mathrm{q}=-\mathrm{Q} / 2$
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