Question

An electric dipole of length $2\text{cm}$ is placed with its axis making an angle of ${30}^{\circ }$ to a uniform electric field having intensity ${10}^5\text{N/C}$. If it experiences a torque of $10\sqrt{3}\text{N-m}$, then the potential energy of the dipole is

• A. $-10\text{J}$
• B. $-20\text{J}$
• C. $-30\text{J}$
• D. $-40\text{J}$

Answer 1

The correct option is C $-30\text{J}$

Given:
$E={10}^5\text{N/C};\tau =10\sqrt{3}\text{N-m}$
$l=2\text{cm}=2\times {10}^{-2}\text{m};\theta ={30}^{\circ }$


Magnitude of torque of dipole in electric field,

$\tau =pE\sin \theta$

$\Rightarrow 10\sqrt{3}=p\times {10}^5\times \frac{1}{2}$

$\therefore p=20\sqrt{3}\times {10}^{-5}\text{C-m}$

Now potential energy of the dipole at the given position

$U=-\overrightarrow{p}.\overrightarrow{E}=-pE\cos \theta$

$\Rightarrow U=-(20\sqrt{3}\times {10}^{-5})\times \left({10}^5\right)\times \cos {30}^{\circ }$

$\Rightarrow U=-20\sqrt{3}\times \frac{\sqrt{3}}{2}=-30\text{J}$

So, $\left(c\right)$ is correct option.

$\begin{array}{c}\text{Why this question}?\\ \text{Tip: For angle between}\overrightarrow{p}and\overrightarrow{E},\theta <{90}^{\circ }\\ \text{the P.E of dipole will be negative, which is an}\\ \text{indicative of stability of system}\end{array}$