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 [ array ll 0^ =0, & 90^ =1 0^ =1, & 90^ =0 array ]

Step-by-step solution

Potential energy of an electric dipole with dipole moment p in a uniform electric field E is U = -pE , where is the angle between p and E . Initially aligned parallel to the field, ₁ = 0^ , yielding U₁ = -pE 0^ = -pE . After rotating by 90^ , ₂ = 90^ , giving U₂ = -pE 90^ = 0 . The energy required is the increase in potential energy: U = U₂ - U₁ = 0 - (-pE) = pE . Final answer: pE