# Potential Energy of Dipole In Electric Field

## Electric Dipole In Uniform Electric Field-

Before you go through this article, make sure that you have gone through the previous article on Electric Dipole In Uniform Electric Field.

We have learnt-

• Two equal and opposite forces act on the electric dipole in uniform electric field.
• These two forces form a couple which tries to rotate the dipole in the electric field.
• The torque experienced by the electric dipole in uniform electric field is given by-

In this article, we will discuss the potential energy of dipole in a uniform electric field.

## Potential Energy of Electric Dipole In Uniform Electric Field-

Consider an electric dipole is placed in a uniform electric field E with its dipole moment p making an angle θ with the field as shown.

Two equal and opposite forces act on the dipole which forms a couple. This couple exerts a torque on the dipole which tries to rotate it in the electric field.

The torque experienced by the dipole in the uniform electric field is given by-

If the dipole is rotated through a small angle dθ against the torque acting on it, then the small work done by the external agent is-

The total work done in rotating the dipole from its orientation making an angle θ1 with the direction of electric field to the angle θ2 will be-

This work is stored as the potential energy (U) of the dipole. Thus,

If initially the dipole is oriented  perpendicular to the direction of the electric field (θ1 = 90°) and then brought to some orientation making an angle θ with the field (θ2 = θ), then potential energy of the dipole will be-

### Special Cases-

#### Case-01: Position of Stable Equilibrium-

When θ = 0°, U = -pEcos0° = -pE

Thus, the potential energy of a dipole is minimum when its dipole moment is parallel to the external field. This is the position of stable equilibrium.

#### Case-02: Position of Zero Energy-

When θ = 90°, U = -pEcos90° = 0

Thus, the potential energy of a dipole is zero when it is held perpendicular to the external field.

#### Case-03: Position of Unstable Equilibrium-

When θ = 180°, U = -pEcos180° = +pE

Thus, the potential energy of a dipole is maximum when its dipole moment is anti-parallel to the external field. This is the position of unstable equilibrium.