Question

Define electric dipole and give the formula for its dipole moment. Find the expression of torque acting on an electric dipole placed in a uniform electric field.

Hint:

The torque on an electric dipole in a uniform electric field is maximum when the dipole moment is perpendicular to the field, and zero when the dipole moment is parallel to the field.

Answer 1

An electric dipole consists of two opposite charges of equal magnitude \(+q\) and \(-q\), separated by a distance \(d\). The electric dipole moment \(\vec{p}\) is defined as the product of the charge and the separation distance: \[ \vec{p} = q \cdot \vec{d} \] where: - \(q\) is the magnitude of the charge, - \(\vec{d}\) is the displacement vector pointing from the negative charge to the positive charge. Torque on an Electric Dipole in a Uniform Electric Field.
When an electric dipole is placed in a uniform electric field \(\vec{E}\), it experiences a torque that tends to align the dipole moment with the electric field. The torque \(\vec{\tau}\) is given by: \[ \vec{\tau} = \vec{p} \times \vec{E} \] where: - \(\vec{p}\) is the dipole moment, - \(\vec{E}\) is the electric field.

Step 1: Magnitude of Torque.
The magnitude of the torque is: \[ \tau = p E \sin\theta \] where: - \(p = |\vec{p}|\) is the magnitude of the dipole moment, - \(E = |\vec{E}|\) is the magnitude of the electric field, - \(\theta\) is the angle between the dipole moment and the electric field.

Final Answer: The formula for torque on an electric dipole in a uniform electric field is: \[ \tau = p E \sin\theta. \]