Question

The maximum torque that a dipole of dipole moment $2\times {10}^{-9}\text{Cm}$ would experience in a uniform electric field of magnitude $4\text{N/C}$ is

$[$0.77 Mark$]$

• A. $28\times {10}^{-10}\text{Nm}$
• B. $8\times {10}^{-9}\text{Nm}$
• C. $81\times {10}^{-6}\text{Nm}$
• D. $2\times {10}^{-4}\text{Nm}$

Answer 1

The correct option is B $8\times {10}^{-9}\text{Nm}$

As we know from the formula,
$\overrightarrow{\tau }=\overrightarrow{P}\times \overrightarrow{E}\Rightarrow \left|\begin{array}{c}\overrightarrow{\tau }\end{array}\right|=\left|\begin{array}{c}\overrightarrow{P}\times \overrightarrow{E}\end{array}\right|=PE\sin \theta$
$\Rightarrow \left|\begin{array}{c}{\overrightarrow{\tau }}_{max}\end{array}\right|=PE(\text{at}\theta =\frac{\pi }{2})$
$=2\times {10}^{-9}\times 4$
$=8\times {10}^{-9}\text{Nm}$