Question

An electric dipole of length 20 cm having $\pm 3\times {10}^{-3}$ C charge placed at 60 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)

-2$\sqrt{3}$ J

Here,

Length of dipole $2a=20cm=0.2m$

Charge, $q=\pm 3\times {10}^{-3}C$, $\theta ={60}^o$

Torque, $\tau =6Nm$

As, $\tau =pEsin\theta$

or $E=\frac{\tau }{psin\theta }=\frac{\tau }{q\left(2a\right)sin\theta }(\because p=q(2a)$

$\therefore E=\frac{6}{3\times {10}^{-3}\times 20\times {10}^{-2}\times sin{60}^o}=\frac{{10}^5}{5\sqrt{3}}N{C}^{-1}$

Potential energy of dipole, $U=-pEcos\theta =-q\left(2a\right)Ecos\theta$

$⟹U=-3\times {10}^{-3}(20\times {10}^{-2})\frac{{10}^5}{5\sqrt{3}}cos{60}^o=-2\sqrt{3}J$