Derive expression for Torque on a …

The moment of the dipole is directed between -ve charge and + charge. Net force and torque on the system should be zero in equilibrium. Therefore, if Potential Energy is high, the equilibrium will be unstable, and equilibrium will be stable for minimum Potential Energy.

The measure of force which induces an object to rotate around an axis is called the torque. Torque is a quantity of vectors and its path depends on the direction of force on the axis. Torque is given by the formula

→τ=→p×→E

τ = pE sinθ……………………(1)

Potential energy (U) of the system is given as

U = -pE cosθ …………………….(2)

In uniform electric field net force on

(1) Torque can be zero only if θ is 0⁰ or π⁰.

(2) Dipole moment is always zero.

Now let us consider θ = 0 then equation (2) becomes

Potential energy (U) = -pE cos0

U = -pE

Let us consider θ = 180⁰ then equation (2) becomes

U = +pE

∴ PE is high in the case of θ = 180⁰, the equilibrium will be unstable and when θ = 0 then PE is low, so the equilibrium is stable.

Dipole is in constant equilibrium if θ = 0⁰.

A a dipole in stable equilibrium, when Electric filed and dipole moment are perpendicular to each other i.e. the angle between them is zero degree and torque will be maximum.