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Question
Derive the expression for the torque acting on an electric dipole, when it is held in a uniform electric field. identify the orientation of the dipole in the electric field, in which it attains a stable equilibrium.
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Solution
Force acting on −q is −qE.
Force acting on +q is qE.
These two forces are equal and opposite to each other. Hence, a torque on the dipole is developed.
Torque = Force × perpendicular distance between the forces
Or, τ = qE × 2 a sin θ
Or, τ = (q × 2a) E sin θ
∴ τ = PE sin θ
Where P is the dipole moment.
Dipole will attain stable equilibrium when it is oriented along the direction of electric field.
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