Question

An electric dipole of dipole moment $\overrightarrow{p}$ is placed along a uniform electric field $\overrightarrow{E}$. The work done in rotating the dipole slowly by ${90}^{\circ }$ is

• A. $\sqrt{2}pE$
• B. $2pE$
• C. $pE$
• D. $\frac{pE}{2}$

Answer 1

The correct option is C $pE$

Electrostatic field is a conservative field, hence we can use

$W_{\text{elec}}=-\Delta U=U_i-U_f$

Also the dipole is rotated slowly,

$W_{\text{ext}}=-W_{\text{elec}}$

$W_{ext}=U_f-U_i$

$W_{ext}=-pE\cos {\theta }_f-(-pE\cos {\theta }_i)$

$(\because {\theta }_i=0^{\circ }\&{\theta }_f={90}^{\circ })$

$\Rightarrow W_{ext}=-pE\cos {90}^{\circ }+pE\cos 0^{\circ }$

$\therefore W_{ext}=pE$