# Electrostatic Dipole

**ELECTRIC DIPOLE**

A system of two equal and opposite charges separated by a certain distance is called an electric dipole.

Figure represents an electric dipole consisting of two charge – q and + q and separated by distance 2a. This distance is called length of the dipole and is a vector

**Electric dipole moment**

** **It is defined as the product of either charge and the length of the electric dipole.

It is denoted by vector $\overrightarrow{p}$

Unit of Dipole moment is coulomb metre (C m).

**Electric field on axial line of an electric dipole**

** **Consider an electric dipole consisting of charges – q and + q, separated by a distance 2a and placed in free space. Let P be a point on the line joining the two charges (axial line) at a distance r from the centre O of the dipole.

The electric field

Now, q (2a) = p, the magnitude of the electric dipole moment of the dipole.

It may be noted that direction of electric field at a point on axial line of the dipole is from charge –q to +q i.e. same as that of electric dipole moment of the dipole. Therefore, in vector notation,

**When dipole is of very small length **

If the dipole is of small length, such that a^{2} can be neglected as compared to r^{2}. Therefore, for an electric dipole of very small length

**Electric field on equatorial line of an electric dipole**

Consider an electric dipole consisting of charges –q and +q separated by a distance 2a and placed in free space. Let P be a point on equatorial line of the dipole (right bisector of the length of dipole) at a distance r from the centre of the dipole.

Let $\underset{{E}_{A}}{\to}$

$\overrightarrow{E}=\overrightarrow{{E}_{A}}+\overrightarrow{{E}_{B}}$

It may be noted that direction of electric field at a point on the equatorial line of the dipole is from charge +q to –q i.e. opposite to the direction of electric dipole moment of the dipole. Therefore, in vector notation,

**When dipole is of very small length**

If the dipole is of small length, such that a^{2} can be neglected as compared to r^{2}. Therefore, for an electric dipole of very small length,

E =

**Torque on a dipole in a uniform electric field**

Consider an electric dipole consisting of charges – q and +q and of length 2a placed in a uniform electric field

Force on charge – q at A = - q $\overrightarrow{E}$

And force on charge + q at B = q

Thus, electric dipole is under the action of two equal and unlike parallel forces, which gives rise to a torque on the dipole. The magnitude of the torque is given by

$\zeta $

= q E (AN) = q E (2 a sin θ) = q (2a) E sin θ

Or $\zeta $

Here, p = q (2a) is electric dipole moment of the electric dipole

The torque on the dipole tends to align it along the direction of the electric field.

Since electric dipole moment vector

$\zeta =\underset{p}{\to}\times \underset{E}{\to}$

**Note:**

**1. **It may be pointed out that when dipole is placed in uniform electric field, it experiences only a torque. Net force on the dipole is zero.

**2. ** Torque on the dipole becomes zero, when it aligns itself parallel to the electric field.

**3. **Torque on the dipole is maximum, when dipole is placed at right angles to the direction of the electric field.