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 :

• 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 stable equilibrium

Answer 1

Answer: (B), (D)

The correct options are
B in equilibrium if it is closer to $A$ than to $C$
D $B$ can never be in stable equilibrium

Here we see that the plates A and C are grounded and the two capacitors thus formed would have same potential difference. If the plate B is closer to A, then the capacitance $C_{AB}>C_{BC}$.
The upper surface of B will have more charge than the lower surface. As the force of attraction between the plates of capacitor is proportional to $q^2$, there will be a net upward force on B. This can balance its weight.