Question Details

What does an electric dipole experience when it is kept in the non-uniform electric field?

Options

A

Only a force

B

Neither force nor torque

C

Only torque

D

Force and torque both

Correct Answer :

Force and torque both

Solution :

The correct answer is Force and torque both.

To understand why an electric dipole experiences both a force and a torque when placed in a non-uniform electric field, let us analyze the behavior of the dipole's constituent charges under these conditions.

An electric dipole consists of two equal and opposite charges, +q and -q, separated by a small distance 2a.

In a non-uniform electric field, the strength and direction of the electric field vary from point to point. This means that the electric field E1 at the location of charge +q is different from the electric field E2 at the location of charge -q (i.e., E1E2).

1. Experience of Force:
The electrostatic force acting on the positive charge is:
F1=qE1
The electrostatic force acting on the negative charge is:
F2=-qE2
The net force Fnet acting on the dipole is the vector sum of these two forces:
Fnet=F1+F2=qE1-qE2=q(E1-E2)
Since E1E2, the net force is not zero (Fnet0). Thus, the dipole experiences a net translational force, causing it to move in the direction of the stronger or weaker field depending on its orientation.

2. Experience of Torque:
Unless the dipole's axis is perfectly aligned with the direction of the electric field gradient and the field lines are parallel, the two forces F1 and F2 will act along different lines of action. This separation between the lines of action of the forces creates a couple, which exerts a net torque on the dipole. This torque tends to rotate the dipole to align its dipole moment with the direction of the local electric field.

Consequently, because both the net force and the net torque are non-zero, the dipole experiences force and torque both when kept in a non-uniform electric field.

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