First slide

Electric dipole

Question

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° is

Moderate

A

$\sqrt{2} pE$
B

$\frac{pE}{2}$
C

2pE
D

pE

Solution

When an electric dipole is placed in an electric field $\vec{E}$ , a torque $\vec{τ} = \vec{p} \times \vec{E}$ acts on it. This torque tries to rotate the dipole through an angle.
If the dipole is rotated from an angle $θ_{1} to θ_{2}$ , then work done by external force is given by
$W = pE ({cosθ}_{1} - {cosθ}_{2}) (i) Putting θ_{1} = 0 °, θ_{2} = 90 ° in the Eq. (i), we get W = pE (\cos 0 ° - \cos 90 °) = p E (1 - 0) = p E$

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