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An electric dipole of moment $\vec{p}$ is lying along a uniform electric field $\vec{E}$. The work done in rotating the dipole by $90^\circ$ is :-
A
$\sqrt{2}\,pE$
B
$\dfrac{pE}{2}$
C
$2pE$
D
$pE$
Detailed Solution
Work done in rotating a dipole from angle $\theta_1$ to $\theta_2$ with the field: $W = pE(\cos\theta_1 - \cos\theta_2)$
Initially the dipole lies along the field, so $\theta_1 = 0^\circ$; finally $\theta_2 = 90^\circ$.
$W = pE(\cos 0^\circ - \cos 90^\circ)$
$W = pE(1 - 0)$
$W = pE$
Equivalently, the potential energy changes from $-pE$ to 0, an increase of $pE$.
Initially the dipole lies along the field, so $\theta_1 = 0^\circ$; finally $\theta_2 = 90^\circ$.
$W = pE(\cos 0^\circ - \cos 90^\circ)$
$W = pE(1 - 0)$
$W = pE$
Equivalently, the potential energy changes from $-pE$ to 0, an increase of $pE$.