Electric Dipole

An electric dipole is a pair of equal and opposite charges separated by a small distance. The separation between the charges is known as the dipole moment and is denoted by 'p'. The direction of the dipole moment is from negative to positive charge.

Torque on an Electric Dipole

When an electric dipole is placed in an external uniform electric field, it experiences a torque. The torque is defined as the product of the dipole moment and the electric field.

The expression for torque acting on an electric dipole placed in an external uniform electric field can be derived as follows:

- Consider an electric dipole with charges +q and -q separated by a distance 'd' in an electric field E, as shown in the figure below.

- The force on the positive charge is F1 = qE, and the force on the negative charge is F2 = -qE.

- The net force on the dipole is the vector sum of F1 and F2, which is zero.

- However, the forces F1 and F2 are not parallel and produce a torque τ about the center of the dipole.

- The magnitude of the torque is given by τ = pE sin θ, where θ is the angle between the dipole moment and the electric field.

- When the dipole moment is perpendicular to the electric field, θ = 90°, and the torque is maximum, given by τmax = pE.

- When the dipole moment is parallel to the electric field, θ = 0°, and the torque is zero.

- The direction of the torque is perpendicular to both the dipole moment and the electric field, and follows the right-hand rule.

In summary, the torque acting on an electric dipole placed in an external uniform electric field is given by τ = pE sin θ, where p is the dipole moment and E is the electric field. The torque tends to align the dipole moment with the electric field, and is maximum when the dipole moment is perpendicular to the electric field.