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Question

(D) The potential energy $U$ of a dipole in an electric field is given by $U = -pE \cos 	heta$,where $	heta$ is the angle between the dipole moment

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$2pE$

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(D) The potential energy $U$ of a dipole in an electric field is given by $U = -pE \cos 	heta$,where $	heta$ is the angle between the dipole moment $p$ and the electric field $E$.Initially,the dipole is parallel to the field,so $	heta_1 = 0^\circ$.The initial potential energy is $U_1 = -pE \cos(0^\circ) = -pE$.Finally,the dipole is anti-parallel to the field,so $	heta_2 = 180^\circ$.The final potential energy is $U_2 = -pE \cos(180^\circ) = -pE(-1) = pE$.The work done by an external agent is equal to the change in potential energy: $W = U_2 - U_1$.$W = pE - (-pE) = 2pE$.

$A$ molecule with a dipole moment $p$ is placed in an electric field of strength $E$. Initially,the dipole is aligned parallel to the field. If the dipole is to be rotated to be anti-parallel to the field,the work required to be done by an external agent is:

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