Question

The work done by an external force in rotating dipole of dipole moment $\overrightarrow{P}$ slowly in uniform electric field of intensity $\overrightarrow{E}$ from $0^0$ to ${180}^0$

• A. $\text{2 PE}$
• B. $\text{8 PE}$
• C. $\text{9 PE}$
• D. $\text{5 PE}$

Answer 1

The correct option is A $\text{2 PE}$

Work done by an external force in rotating dipole of dipole moment $=\overline{P}$

Uniform electric field of intensity $\overline{E}$ from $0^0$ to ${180}^0$

The work done is given by $dw=T\times d\left(\theta \right)$

Torque at any particular angle $T.E\times q\times d\sin \theta$

total work done $=\left[INT\right]\left(dw\right)$

$=\left[INT\right](E\times d\times q\sin \theta )d\left(\theta \right)$

$=Eqd(-1-1)$

$=2Eqd$ will be the required

$=2PE$ ($\because$ $qd=p$)