Work Done To Rotate A Dipole In External Electric Uniform Field

We have learned in detail about magnetism, electricity, the electric field, and many other interesting topics in our previous articles. We have come across many topics like a uniform field, the strength of the field, magnetic poles, the orientation of magnets, and many more. Let us know more about the dipole and its effect on the electric field. An electric dipole is seen when the positive and negative charges are found separated in any electromagnetic system.

Example of dipole: Consider a pair of electric charges with opposite signs having equal magnitude, separated by a small distance. The magnitude of an electric dipole is given as:

Where q is the magnitude of each charge and d is the distance between them.

We know that a dipole, when kept in an external electric field, experiences a rotating effect. The force that causes the rotating effect is known as the torque on the dipole. Torque is a vector quantity that is given by the formula:

The field in which the strength remains the same at all points is known as the uniform electric field. In a uniform electric field, the field strength does not change, and the field lines tend to be parallel and are equally spaced.

Since the force magnitudes are equal and are separated by a distance d, the torque on the dipole is given by the formula:

Torque (τ) = Force × distance separating forces

τ = Fd sinθ = qEd sinθ = pE sinθ

The torque on electric dipole is given by

Let us know about the work done to rotate a dipole in an external electric uniform field.

Work Done To Rotate A Dipole In External Electric Uniform Field

A pair of force which is equal in magnitude, with opposite direction, and displaced by perpendicular distance or moment is known as the couple.

When a couple acts on a dipole, the torque on dipole will be

Work done to rotate a dipole is given by

Total work done is given by

When the dipole is rotated from 0 to θ degrees, work done is given by

Since cos 0 = 1

Hence, the work done to rotate a dipole in an external electric uniform field is

Work done if dipole rotated from 90 degree

Since cos 90 = 0

Work done if dipole rotated from 180 degree

When

The dipole is said to be stable when the dipole is aligned in the direction of the electric field.

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