First slide

Capacitors and capacitance

Question

An air capacitor consists of two identical parallel plates A and B as shown in figure. Plate A is given change Q and plate B is given a charge 3Q . P is the median plane of the capacitor. If $C_{0}$ is the capacitance of the capacitor then

Moderate

A

$V_{P} - V_{A} = \frac{Q}{4 C_{o}}$
B

$V_{P} - V_{A} = \frac{Q}{2 C_{o}}$
C

$V_{P} - V_{A} = \frac{- Q}{C_{o}}$
D

$V_{P} - V_{B} = \frac{- Q}{4 C_{o}}$

Solution

The distribution of charges on plates are
E at any point between the plates is
$E = \frac{σ}{2 \in_{0}} + \frac{σ}{2 \in_{0}} = \frac{σ}{\in} = \frac{Q}{A \in_{o}}$
$d v = - E . d r$
$\Rightarrow V_{A} - V_{P} = - \frac{Q}{A \in_{o}} \times \frac{d}{2}$
$∴ V_{P} - V_{A} = \frac{Q}{2 C_{o}}$

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