First slide

Electrostatic potential

Question

A, B and C are three large, parallel conducting plates, placed horizontally. A and C are rigidly fixed and earthed. B is given some charge. Under electrostatic and gravitational forces, B may be

Difficult

A

in equilibrium midway between A and C
B

in equilibrium if it is closer to A than to C
C

in equilibrium if it is closer to C than to A
D

B can never be in equilibrium

Solution

A and C are at zero potential.
$∴$ Potential differences $V_{BA} = V_{BC}$

Plate B will be in equilibrium only if $F_{A} = m g + F_{C}$
( $F_{A}$ and $F_{C}$ respectively are the forces of attraction on plate B by plate A and C )
This means $F_{A} > F_{C}$ . This is possible only if electric field $(E = \frac{V}{d})$ in the gap AB is more than that of the electric field in the gap BC .
$∵ V_{BA} = V_{BC}$
$∴ d_{BA} < d_{BC}$
Therefore, the correct answer is (B)

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