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An electric dipole of dipole moment p is aligned parallel to a uniform electric field E. The energy required to rotate the dipole by 90° is

Asked in Karnataka NEET 2013 · Torque, energy and work done

(1) p²E
(2) pE
(3) infinity
(4) pE²

Answer: (2) pE

Step-by-step solution

Work needed to turn a dipole from θ₁ to θ₂: W=pE(cos θ₁-cos θ₂).

Here θ₁=0° (parallel) and θ₂=90°.

W=pE(1-0)=pE.

Why the other options are wrong

(1) Dimensionally wrong: pE is an energy, so p²E carries an extra factor of dipole moment.
(3) The torque on the dipole is finite (at most pE), so turning it through a finite angle needs finite work.
(4) Dimensionally wrong: pE² carries an extra factor of field.

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