JEE Main 2025 · 29 January · evening · Single correct · +4 / −1
An electric dipole is placed at a distance of 2 cm from an infinite plane sheet having positive charge density σₒ. Choose the correct option from the following.
- (a) Torque on dipole is zero and net force is directed away from the sheet.
- (b) Potential energy of dipole is minimum and torque is zero.
- (c) Potential energy and torque both are maximum.
- (d) Torque on dipole is zero and net force acts towards the sheet.
Answer and solution
Answer (b) Potential energy of dipole is minimum and torque is zero.
Solution
Physics sir · 5 steps
Find the angle between the dipole and the sheet's field, and remember that field is uniform.
- Field of the sheet. An infinite sheet with positive σ₀ gives a field E = σ₀/2ε₀, pointing away from the sheet. Its size is the same at every distance, so the field is uniform.
- Dipole direction. The dipole moment p⃗ points from -q to +q. In the figure -q is nearer the sheet and +q is farther away, so p⃗ points away from the sheet, along E⃗. The angle between them is θ = 0.
τ = pE sin 0° = 0, U = -pE cos 0° = -pE
- Torque and energy. Torque is zero, and U = -pE is the lowest value -pE cos θ can take. This is stable equilibrium.
- Net force. In a uniform field, +q feels qE away from the sheet and -q feels qE towards it. The two forces cancel, so the net force is zero.
- So. Potential energy is minimum and torque is zero, which is option (b).
The idea to keep. A dipole aligned with the field (θ = 0) has zero torque and minimum energy. In a uniform field, like that of an infinite sheet, the net force on any dipole is zero.
Answer from the NTA final answer key. Solution by PrepWiser.