Concept Of Dipole In A Uniform External Field

A pair of equal and opposite charges placed at a certain distance, d is known as an Electric Dipole. 

When these pairs of charges are placed in a uniform external field, a rotational force is produced due to the electric field, which is also known as torque.

The torque is responsible for aligning the dipoles in a uniform external field so that the net torque on the dipole would result from zero.  A permanent dipole of dipole moment p in a uniform external field experiences a torque having a zero effect that corresponds with the presence of an electric field.

Concept of Electric Dipole:

An electric dipole is a pair of charges separated by a distance, let’s say d.

This pair is equal but opposite in nature of charges, so together, we call them electric-dipoles. An electric dipole is important to understand the concept of polarity. If the dipole is small in a system of charges, either the charges are small, or the distance/ separation between them is small.

Dipole in a uniform external field – Electric force on a dipole example:

When we place an electric dipole in an uniform external field, i.e, where the electric field is uniform, then due to external force( that is, electric field), torque is produced at a point on the field which acts on the dipole. 

There are molecules or charges in which the dipole moment is zero at its centre. But when they are introduced in an electric field, a dipole moment is produced.

But charges that have some value of dipole moment before the electric field is introduced are the charges that have a definite dipole moment value before an external field is passed. Such charges are called polar charges.

These charges have a permanent dipole of dipole moment p in a uniform external field moment.

Now, when an electric field is introduced on these charges, a force is acted on charge +q and on -q.

A force of +qe acts on the charge +q, and a force of -qe acts on the -q charge. 

This way, the net force on the dipole becomes zero, as the electric field is uniform.

But when the electric dipole is not placed under a uniform external electric field, then what would happen to torque?

This time, evidently the net force on the dipole would not be zero. 

Torque on an Electric Dipole:

Torque = force х distance separating forces

= qe sinӨ x d

This is as per Magnitude of torque formula.

Since the dipole moment, p is the measure of separation of two charges. 

Hence, p = qd

= p E sinӨ = pE

Thus, we can define torque as a vector quantity that arises due to placing an electric dipole in an external electric field.

Here, Torque is the vector product of dipole moment and electric field.

This torque can be maximum or minimum under different conditions.

Let us understand the cases involved when torque gets maximum and when it gets minimum.

When torque is minimum:

When the direction of the dipole moment is parallel to the external electric field then the angle between the both becomes zero.

This means, θ = 0˙

And sin 0= 0˙

Hence, torque in this case would be equal to zero. 

In this case, the dipole is in stable equilibrium.

When torque is maximum:

When the direction of the dipole moment is antiparallel to the external electric field that is opposite to the electric field. That is when torque is held perpendicular to the external electric field then it becomes maximum.

This means, θ= 90o,

Sin 90o= 1

Hence, the torque, in this case, would be maximum.

And the dipole would be in unstable equilibrium.

Physical Significance Of an Electric Dipole:

It gives a measure of the polarity/polarisation of a system having charges. The concept of dipole moment which comes to play after understanding electric dipole is the next simplest piece of information to know about the measure of separation of charges in a system. The torque produced due to placing the dipole in an external electric field measures the tendency of a dipole to align with an external electric field. 

In this way we get to know about various phenomena by the single concept, that is electric dipole.

Conclusion

A pair of equal and opposite charges is called an electric dipole. When an electric dipole is positioned in a uniform external field then a rotational force acts on the dipole which forces the dipole to align in such a way that torque acting on it would get zero. But there are certain cases where this torque would not get zero. That case arises when the same dipole is positioned in a non-uniform external electric field.