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 ${10}^5\text{N/C}$.If it experiences a torque $10\sqrt{3}\text{Nm}$,then potential energy of the dipole

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

Answer 1

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

Torque acting on a dipole, $\tau =pE\sin {30}^{\circ }$

Substituting the data given in the question,

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

$\Rightarrow p=2\sqrt{3}\times {10}^{-4}\text{Cm}$

Potential energy of a dipole, $U=-pE\cos {30}^{\circ }$

$U=-2\sqrt{3}\times {10}^{-4}\times {10}^5\times \frac{\sqrt{3}}{2}$

$\Rightarrow U=-30\text{J}$

Hence, option (d) is the correct answer.