An electric dipole of moment overrightarrow{p | vedclass

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Question

(A) The potential energy $U$ of an electric dipole in an external electric field is given by $U = -\overrightarrow{p} \cdot \overrightarrow{E} = -pE \

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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 $U = -\overrightarrow{p} \cdot \overrightarrow{E} = -pE \cos 	heta$.Initially,the dipole is lying along the electric field,so $	heta_1 = 0^{\circ}$.Initial potential energy $U_1 = -pE \cos 0^{\circ} = -pE(1) = -pE$.Finally,the dipole is rotated by $90^{\circ}$,so $	heta_2 = 90^{\circ}$.Final potential energy $U_2 = -pE \cos 90^{\circ} = -pE(0) = 0$.The work done $W$ is equal to the change in potential energy: $W = U_2 - U_1$.$W = 0 - (-pE) = pE$.

An electric dipole of moment $\overrightarrow{p}$ is lying along a uniform electric field $\overrightarrow{E}$. The work done in rotating the dipole through $90^{\circ}$ is $\left[\sin 0^{\circ}=\cos 90^{\circ}=0, \cos 0^{\circ}=\sin 90^{\circ}=1\right]$

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