Question

A light rod is hinged (free to rotate) at its centre $O$ as shown in figure. Two point charges of same magnitude $+q$ are kept at its two ends. Rod is placed in uniform electric field $E$ as shown. Space is gravity free. Net torque about the hinge is

• A. $2rqE$
• B. $4rqE$
• C. $3rqE$
• D. Zero

Answer 1

The correct option is D Zero

FBD of two charges in uniform electric field is shown in the figure.


Torque on upper charge about hinge point $\left(O\right)$,

${\tau }_1=rF\sin {90}^{\circ }=rF=rqE\text{(clockwise)}$

Torque on lower charge about hinge point $\left(O\right)$,

${\tau }_2=rF\sin {90}^{\circ }=rF=rqE\text{(anticlockwise)}$

Net torque at point $O$, taking clockwise torque positive,

${\tau }_{\text{net}}={\tau }_1+(-{\tau }_2)=rqE-rqE=0$

Therefore option $\left(d\right)$ is correct.