# Potential energy of a dipole in an external field

Safalta Expert Published by: Noor Fatima Updated Sat, 22 Oct 2022 11:33 AM IST

## Highlights

Here is important and relevant information regarding Class 12 Physics Concept of Potential energy of a dipole in an external field Read the article to learn about the same.

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Potential energy of a dipole in an external field: Assume a dipole with charges q1 = +q and q2 = -q kept in a uniform electric field, as shown in the figure above. The charges are divided by a distance d, and the magnitude of an electric field is E.

The force applied on the charges is given as –qE, and +qEas can be observed in the figure. As we are well aware that when a dipole is kept in a uniform electric field when any force on the charge is not applied, but it experiences a force equal to τ which is expressed as
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This force revolves around the dipole unless it is kept parallel or anti-parallel to the field.

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If we apply an external and opposite force, it balances the impact of this torque expressed as τext. It revolves the dipole from the angle Ɵ0 to an angle Ɵ1 at a minute angular speed without any angular acceleration.

The amount of work performed by the external torque can be expressed as-

As we are aware that the work performed in bringing a system of charges from infinity to a defined configuration is referred to as the potential energy of the system. Therefore,

The potential energy U (Ɵ) can be related to the inclination Ɵ of the dipole using the above relationship.

From the equation mentioned above, we can observe that the potential energy of the dipole kept in an external field is zero when the angle Ɵ  is equal to 90°  or when the dipole makes a right angle, i.e.,  90°.

Electric Charges and Static Electricity
Electric Charge
Conductors and Insulators
Basic Properties of Electric Charge
Forces between Multiple Charges
Charging by Induction
Magnetic effect of Electric Current
Electric Flux
Electric Dipole

Assuming the initial angle at which the potential energy is nil,

The potential energy of the system is expressed as-
Candidates can refer to the information given above about Potential energy of a dipole in an external field.

## What is p in the potential energy of a dipole?

P is the dipole moment of the electric dipole.

## Is dipole moment a scalar quantity?

No, the dipole moment is a vector quantity.

## What is the potential energy in an external field?

The work needed to move the charge from infinity to the point is equivalent to the potential energy of the charge q in the field.

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