Question

An electric dipole of length $20 \,cm$ having $\pm 3 \times10^{-3}\,C$ charge placed at $60^{\circ}$ with respect to a uniform electric field experiences a torque of magnitude $6\, N\, m$. The potential energy of the dipole is

• A. $-2 \sqrt{3}\, J$
• B. $5\sqrt{3}\,J$
• C. $-3 \sqrt{2}\,J$
• D. $3 \sqrt{5}\, J$

Answer 1

Answer: (A)

Here, length of dipole, $2a = 20 \,cm = 20 \times 10^{-2}\, m $
Charge $q =\pm\, 3\times10^{-3}\, C, \theta=60^{\circ}$ and torque $\tau=6\,N\,m$
As $\tau=PEsin \theta$
or $E=\frac{\tau}{P\,sin\,\theta}=\frac{\tau}{q\left(2a\right)sin\,\theta} \left(\because p=q\left(2a\right)\right)$
$\therefore E=\frac{6}{3\times10^{-3}\times20\times10^{-2}\times sin\,60^{\circ}}=\frac{10^{5}}{5\sqrt{3}}N \,C^{-1}$
Potential energy of dipole, $U =-pEcos\theta=-q\left(2a\right)Ecos\theta$
$=-3\times10^{-3}\left(20\times10^{-2}\right)\frac{10^{5}}{5\sqrt{3}}cos\,60^{\circ}$
$=\frac{-3\times10^{-5}\times20\times10^{5}}{5\sqrt{3}\times2}$
$=-2\sqrt{3}\,J$