Question

An electric dipole with dipole moment ' $p$ ' is placed with its axis at $30^{\circ}$ to a uniform electric field. The work done in rotating the dipole to a position where its axis is perpendicular to the field is

• A. $2 p E$
• B. $\frac{2 p E}{\sqrt{3}}$
• C. $\frac{\sqrt{3} p E}{2}$
• D. $0$

Answer 1

Answer: (C)

Given, for an electric dipole,
$\theta_{1}=30^{\circ}$
$\theta_{2}=90^{\circ}$
$\therefore $ Work done in rotating the dipole from $\theta_{1}=30^{\circ}$ to a position, where its axis is perpendicular
$\left(\theta_{2}=90^{\circ}\right)$ to electric field is given as
$W=p E\left(\cos \theta_{1}-\cos \theta_{2}\right)$
$=p E\left(\cos 30^{\circ}-\cos 90\right)$
$=p E\left(\frac{\sqrt{3}}{2}-0\right)=\left(\frac{\sqrt{3}}{2} p E^{\circ}\right)$