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

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$pE$

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(A) The potential energy $U$ of an electric dipole in an external 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 aligned parallel to the electric field,so $	heta_1 = 0^{\circ}$.The initial potential energy is $U_1 = -pE \cos 0^{\circ} = -pE(1) = -pE$.Finally,the dipole is rotated by $90^{\circ}$,so $	heta_2 = 90^{\circ}$.The final potential energy is $U_2 = -pE \cos 90^{\circ} = -pE(0) = 0$.The work done (energy required) to rotate the dipole is equal to the change in potential energy: $W = \Delta U = U_2 - U_1$.$W = 0 - (-pE) = pE$.

An electric dipole of dipole moment $p$ is aligned parallel to a uniform electric field $E$. The energy required to rotate the dipole by $90^{\circ}$ is $\left[\begin{array}{ll}\sin 0^{\circ}=0, & \sin 90^{\circ}=1 \\ \cos 0^{\circ}=1, & \cos 90^{\circ}=0\end{array}\right]$

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