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2. Electric potential and capacitance — Physics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 SciencePhysics2. Electric potential and capacitance1 Mark
MCQ
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 :-
  • ✓
    $-Q/2$
  • B
    $-Q$
  • C
    $+Q$
  • D
    $+2Q$
✓

Answer

Correct option: A.
$-Q/2$
a
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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