Question

An electric dipole of dipole moment $P$ is placed parallel to a uniform electric field of magnitude $E.$ The amount of work done in slowly rotating the dipole by ${60}^{\circ }$ will be

$[$0.77 Mark$]$

• A. $2PE$
• B. $PE$
• C. $\frac{PE}{4}$
• D. $\frac{PE}{2}$

Answer 1

The correct option is D $\frac{PE}{2}$

As we know that,
$U=-\overrightarrow{P}.\overrightarrow{E}$
$W=\Delta U=-PE\cos {\theta }_2-(-PE\cos {\theta }_1)$
$=PE(\cos {\theta }_1-\cos {\theta }_2)$
$=PE(\cos 0^{\circ }-\cos {60}^{\circ })$
$=\frac{PE}{2}$

hence, option (d) is the correct answer