An electric dipole is placed at an angle of ${30}^0$with an electric field intensity $2\times {10}^5 N{C}^{-1}$. It experiences a torque equal to $4 Nm$. The charge on the dipole, if the dipole length is $2cm$

When a dipole is placed in electric field, it experiences torque given by

$\mathrm{\tau }=\mathrm{PEsin}\mathrm{\theta }$

P = dipolemoment = d × q

E = intensity of electric field

$\theta$ = angle between P and E

$\mathrm{\tau }=\mathrm{PEsin}\mathrm{\theta }$

$\mathrm{\tau }=\mathrm{d}\times \mathrm{q}\times \mathrm{E}\times \sin \mathrm{\theta }$

$\mathrm{q}=\frac{\mathrm{\tau }}{\mathrm{dEsin}\mathrm{\theta }}=\frac{4}{2\times {10}^{-2}\times 2\times {10}^5\times \frac{1}{2}}$

$\mathrm{q}=2\times {10}^{-3}\mathrm{C}$

= 2 mC