Question

Find the maximum value of torque acting on the dipole placed in a uniform electric field as shown in figure.

• A. ${10}^{-6}\text{N-m}$
• B. $2\times {10}^{-6}\text{N-m}$
• C. $3\times {10}^{-6}\text{N-m}$
• D. Data insufficient

Answer 1

The correct option is A ${10}^{-6}\text{N-m}$

Given:
$E=200\text{N/C};q=10\text{nC};d=0.5\text{m}$

We know that, the torque acting on a dipole in a uniform electric field is given by

$\overrightarrow{\tau }=\overrightarrow{p}\times \overrightarrow{E}$

So, the magnitude of torque,

$\tau =pE\sin \theta$

For maximum value, $\sin \theta =1$

$\therefore {\tau }_{\text{max}}=pE=qdE$

$\Rightarrow {\tau }_{\text{max}}=10\times {10}^{-9}\times 0.5\times 200$

$\Rightarrow {\tau }_{\text{max}}={10}^{-6}\text{N-m}$

Hence, option $\left(a\right)$ is the correct choice.