Question

An electric dipole of length 10 cm having charge $6\times {10}^{-3}$ C, placed at ${30}^0$ with respect to a uniform electric field , experience energy of electric field , experience a torque of magnitude $6\sqrt{3}$ Nm. Calculate (i) magnitude of electric field and (ii) potential energy of electric dipole.

Answer 1

The two charges $(q=6\times {10}^{-3}C$ each) of the dipole are situated at a distance $d=10cm=0.1m$

Dipole moment :

$P=qd=6\times {10}^{-3}\times 0.1$

$P=6\times {10}^{-4}cm$

Let the dipole makes angle $\theta ={30}^o$ with the electric field $E$.

As torque on the dipole = $\tau =6\sqrt{3}$, so,

$\tau =PE\sin \theta$

$\Rightarrow 6\sqrt{3}=6\times {10}^{-4}\times E\times \sin \left({30}^o\right)$

$\Rightarrow E=2\sqrt{3}\times {10}^{4}N/C$.

and potential energy of dipole:

$u=-pE\cos \theta$

$=-6\times {10}^{-3}\times 2\sqrt{3}\times {10}^4\times \cos \left({30}^o\right)$

$\Rightarrow u=-180T$