Question

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

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

Answer 1

The correct option is D $2\text{mC}$

Given:
$\tau =4\text{Nm};2l=2\text{cm}=0.02\text{m}$
$E=2\times {10}^5\text{N/C};\theta ={30}^{\circ }$


As we know that,

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

$\Rightarrow \tau =pE\sin \theta$

putting the given value in above expression, we get

$\Rightarrow 4=p\times 2\times {10}^5\sin {30}^{\circ }$

$\Rightarrow p=4\times {10}^{-5}\text{Cm}$

We know that, $p=q\left(2l\right)$
$\Rightarrow q\left(2l\right)=q\times 0.02=4\times {10}^{-5}$

$\Rightarrow q=2\times {10}^{-3}=2\text{mC}$

Hence, option $\left(d\right)$ is correct.