Special Cases of Dipole Experiencing a Torque in Uniform Electric Field

When a dipole is placed in a uniform electric field, it experiences a torque that tends to align it with the direction of the field. However, there are certain special cases where the behavior of the dipole is different. These cases are discussed below:

1. Parallel to Electric Field

When a dipole is placed parallel to the electric field, it experiences no torque. This is because the electric field acts on both the positive and negative charges of the dipole in the same direction, and hence the net force on the dipole is zero. As a result, the dipole does not experience any rotation and remains in its initial orientation.

2. Perpendicular to Electric Field

When a dipole is placed perpendicular to the electric field, it experiences a maximum torque. This is because the electric field acts on the charges of the dipole in opposite directions, resulting in a net force that is perpendicular to the dipole moment. As a result, the dipole experiences a torque that tends to rotate it such that its dipole moment aligns with the direction of the field.

3. Inclined to Electric Field

When a dipole is placed at an angle to the electric field, it experiences a torque that tends to rotate it such that its dipole moment aligns with the direction of the field. The magnitude of the torque is given by the equation τ = pEsinθ, where p is the dipole moment, E is the electric field strength, and θ is the angle between the dipole moment and the electric field.

4. Anti-parallel to Electric Field

When a dipole is placed anti-parallel to the electric field, it experiences a torque that tends to rotate it such that its dipole moment aligns opposite to the direction of the field. This is because the electric field acts on the charges of the dipole in opposite directions, resulting in a net force that is perpendicular to the dipole moment. As a result, the dipole experiences a torque that tends to rotate it such that its dipole moment aligns opposite to the direction of the field.

Conclusion

The behavior of a dipole in a uniform electric field depends on the orientation of the dipole with respect to the direction of the field. The dipole experiences no torque when it is parallel to the field, a maximum torque when it is perpendicular to the field, and a torque that depends on the angle between the dipole moment and the field when it is inclined to the field. When the dipole is anti-parallel to the field, it experiences a torque that tends to align its dipole moment opposite to the direction of the field.