Question

An electric dipole of length $4\text{cm}$ , when placed with its axis making an angle of ${60}^{\circ }$ with a uniform electric field , experiences a torque of $4\sqrt{3}\text{Nm}$. Find the potential energy of the dipole, if the dipole has charges of $\pm 8\text{nC}$ (in $\text{J}$)​​​​​​​

Answer 1

Given,

Charge of dipole , $q=\pm 8\times {10}^{-9}\text{C}$

Seperation between the charges $2a=4\text{cm}\text{or}0.04\text{m}$

Torque acting on dipole $\tau =4\sqrt{3}\text{Nm}$

Angle made by the axis of dipole with uniform electric field , $\theta ={60}^{\circ }$

We know that,

Torque on the electric dipole is given by $\tau =pE\sin \theta$

$\Rightarrow E=\frac{\tau }{p\sin \theta }=\frac{4\sqrt{3}}{3.2\times {10}^{-10}\times \sin {60}^{\circ }}$

$\Rightarrow E=\frac{4\sqrt{3}\times 2}{3.2\times {10}^{-10}\times \sqrt{3}}=2.5\times {10}^{10}\text{N/C}$

Potential energy of the electric dipole is
$$U=-pE\cos \theta$$
Substituting the given data we get,
$U=-3.2\times {10}^{-10}\times 2.5\times {10}^{10}\times \cos {60}^{\circ }$

$\Rightarrow U=-3.2\times 2.5\times 0.5$

$\Rightarrow U=-4\text{J}$

Accepted answer : $-4$