Question

A light rod is hinged (free to rotate) at its centre $O$ as shown in figure. Two point charges of same magnitude $+q$ are kept at its two ends. The rod is placed in uniform electric field $E$ as shown. Space is gravity free. The equilibrium is

• A. stable
• B. unstable
• C. neutral
• D. not in equilibrium

Answer 1

The correct option is C neutral

FBD of two charges in uniform electric field is shown in figure.

Two charges are in equilibrium because the net force of $2qE$ on the charges is balanced by hinge force.

Also, net torque about the hinge point $\left(O\right)$ is zero as $F_1$ force produces torque in clockwise while $F_2$ produces torque of equal magnitude $\left(rqE\right)$ in anticlockwise.

Here, if we displace the rod, then also the net force and net torque are zero.
Hence, it will have no tendency to come back or go away from equilibrium position.
Thus, it is in neutral equilibrium.