Question

An electric dipole is placed at an angle of ${30}^o$ with an electric field intensity $2\times {10}^{5}N/C$. It experiences a torque equal to $4Nm.$ The charge on the dipole, if the dipole length is $2cm$, is :

• A. $7\mu C$
• B. $8mC$
• C. $2mC$
• D. $5\mu C$

Answer 1

The correct option is C $2mC$

$\text{Step 1: Dipole moment of dipole}$

Given the dipole length $l=2cm=2/100m$

So, the Dipole moment of dipole will be

$P=lq$ $=\left(2/100\right)q$

$P=0.02q$

$\text{Step 2: Torque acting on dipole}$

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

$\Rightarrow \tau =PE\sin \theta$

Or, $4Nm=\left(0.02q\right)(2\times {10}^{5}N/C)\sin {30}^o$

Or, $q=200\times {10}^{-5}C$ $=2mC$

Hence, Option C is correct