Derivation of Torque on an Electric Dipole

Consider a dipole with charges +q and –q that form a dipole because they are separated by a distance of d. Place it in a homogeneous electric field of strength E, with the dipole’s axis forming an angle θ with the electric field.

The force on the charges, F = ± q E

The components of the force perpendicular to the dipole, F = ± q E sinθ

Since these components are equal and are separated by a distance d, the torque on the dipole is:

Torque = Force × distance between forces

τ = (q E sinθ) d = q d E sinθ

Since ‘qd’ is the magnitude of dipole moment (p), and the direction of dipole moment is from positive to negative charge; torque is the cross product of dipole moment and electric field. If the direction of an electric field is positive, the torque is in the clockwise direction (therefore negative) in the above figure.

Thus,

τ = – p E sinθ

The negative sign shows that torque is in the clockwise direction.

Science is a strange subject that never ceases to amaze you as new subjects are presented. We’re all aware that charge occurs everywhere around us and that its existence causes a variety of natural events. Furthermore, positive and negative charges exist in many forms, displaying various characteristics in the presence of a stimulating field.

Have you ever come across the term “electric dipole”? This unusual configuration of electric charges, i.e., positive and negative charges, creates an intriguing physics idea. To be more specific, Electric Dipole is a separation of positive and negative charges.

Consider a pair of electric charges with opposite signs but equal magnitude that are separated by a much smaller distance. The behavior of an Electric Dipole in the presence of an external field is now our main focus. Let’s review the characteristics of the torque acting on an electric dipole in a uniform electric field before moving on to the properties of the torque acting on an electric dipole in a uniform electric field.