What is an electric dipole? Derive an expression for the torque act...

Question

What is an electric dipole? Derive an expression for the torque acting on an electric dipole when held in a uniform electric field. Hence, define the dipole moment.

Accepted Answer

Electric Dipole:
An electric dipole is a system of two equal and opposite point charges (+q and -q) separated by a small distance 2l.

Dipole moment: p = q × 2l
Direction: from -q to +q

Derivation of Torque on a Dipole in Uniform Field

Setup:
Place the dipole in a uniform electric field E. Let the dipole make an angle θ with the field.

Step 1: Forces on each charge
• Force on +q: F₁ = qE (in direction of E)
• Force on -q: F₂ = qE (opposite to E)

Step 2: Net force
F_net = qE - qE = 0

Step 3: The two forces form a couple
Although net force is zero, the two forces produce a torque (turning effect).

Step 4: Calculate torque
Torque = (magnitude of force) × (perpendicular distance between forces)

Perpendicular distance = 2l sinθ

τ = qE × 2l sinθ
τ = (q × 2l) × E × sinθ
τ = pE sinθ

Vector form:
τ = p × E

Definition of Dipole Moment from torque:
When E = 1 unit and θ = 90°, then τ = p.

Hence, dipole moment is defined as the torque acting on a dipole when placed perpendicular to a unit electric field.

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