Question

There are two possible alignments of a dipole in an external electric field where the dipole is in equilibrium: when the dipole moment is parallel to the electric field and when the dipole moment is oriented opposite the electric field.
Part A
Are both alignments stable? (Consider what would happen in each case if you gave the dipole a slight twist.)
a) Yes
b) No
Part B
Based on your answer to the previous part and your experience in mechanics, in which orientation does the dipole have less potential energy?
a) The arrangement with the dipole moment parallel to the electric field has less potential energy.
b) The arrangement with the dipole moment opposite the electric field has less potential energy.
c) Both arrangements have the same potential energy.

Answer 1

Answer:

A. (b)

B. (a)

Explanation:

The electric dipole moment is the product of charge and the length of the dipole.

The torque on the dipole placed in the external electric field is given by

torque = p E sin A

where, p is the electric dipole moment, E is the electric field, A is the angle between the field and dipole moment.

When the dipole moment is parallel to the electric field, the net torque is zero and it is said to be in stable equilibrium.

When the dipole moment is anti parallel to the electric field, the net torque is zero but the dipole is in unstable equilibrium.

So, the option (b) is correct.

Teh energy is given by

U = - p  E cos A

When the angle A is zero , the potential energy is negative and it is minimum.