JEE Physics 2025 Question with Solution

Given: An electric dipole is placed near an infinite plane sheet with positive surface charge density $\sigma$ at a distance of $2 \, \text{cm}$.

Find: The correct statement about torque, force, and potential energy of the dipole.

The electric field due to an infinite plane sheet of charge is uniform and is given by

$$E = \frac{\sigma}{2\varepsilon_0}$$

This field is directed away from the positively charged sheet.

For a dipole in a uniform electric field:

$$\tau = pE \sin\theta$$

and the potential energy is

$$U = -pE \cos\theta$$

For equilibrium, torque must be zero, so

$$\sin\theta = 0$$

which gives $\theta = 0^\circ$ or $180^\circ$.

When the dipole is aligned with the electric field, that is $\theta = 0^\circ$,

$$U = -pE$$

which is the minimum value of potential energy. In this aligned position, torque is also zero.

Because the electric field of an infinite sheet is uniform, the dipole experiences no net translational force. Hence options mentioning net force toward or away from the sheet are incorrect.

Therefore, the potential energy of the dipole is minimum and the torque is zero. The correct option is C.

Given: The sheet has uniform positive surface charge density $\sigma$, so it creates a constant electric field.

Find: Which option matches the dipole's equilibrium behavior.

The field due to the infinite sheet is

$$E = \frac{\sigma}{2\varepsilon_0}$$

Since this field does not vary with distance, it is uniform at the dipole's location.

A dipole in a uniform field has:

1. Torque

$$\tau = pE \sin\theta$$

2. Potential energy

$$U = -pE \cos\theta$$

Torque becomes zero when the dipole is either parallel or anti-parallel to the field.

For $\theta = 0^\circ$,

$$U = -pE$$

This is the minimum potential energy state.

For $\theta = 180^\circ$,

$$U = +pE$$

This is the maximum potential energy state.

Thus the stable equilibrium configuration is the one with minimum potential energy, where the dipole aligns with the field and the torque becomes zero.

Therefore, the correct option is C: Potential energy of dipole is minimum and torque is zero.