An electric dipole is placed in a uniform electric field E with its...

Question

An electric dipole is placed in a uniform electric field E with its dipole moment p parallel to the field. Find:

(1) The work done in turning the dipole till its dipole moment points in the direction opposite to E.

(2) The orientation of the dipole for which the torque acting on it becomes maximum.

Accepted Answer

Part (1): Work done in rotating the dipole from parallel to antiparallel

Formula:
W = pE(cosθ₁ - cosθ₂)

Given:
• Initial angle θ₁ = 0° (parallel to E)
• Final angle θ₂ = 180° (antiparallel to E)

Calculation:
W = pE(cos 0° - cos 180°)
W = pE(1 - (-1))
W = pE(1 + 1)
W = 2pE

Part (2): Orientation for maximum torque

Formula:
τ = pE sinθ

Condition for maximum:
sinθ = 1, which gives θ = 90°

Conclusion:
The dipole moment p must be perpendicular to the electric field E for maximum torque.

Maximum torque: τ_max = pE

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