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An electric dipole of moment p is initially oriented perpendicular (normal) to a uniform electric field E. The work done in rotating it through 180 degrees is:

1. Zero
2. pE
3. +2pE
4. -2pE

Correct answer: Zero

Solution

U(theta) = -pE cos(theta). Initially the dipole is perpendicular to E, so theta_i = 90 deg and U_i = -pE cos90 = 0. Rotating through 180 deg takes it to theta_f = 90 + 180 = 270 deg, where U_f = -pE cos270 = 0. Work done = U_f - U_i = 0 - 0 = 0.

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