Two point charges $$-4\mu c$$ and $$4\mu c$$, constituting an electric dipole, are placed at (−9, 0, 0)cm and (9, 0, 0)cm in a uniform electric field of strength $$10^{4}NC^{-1}$$. The work done on the dipole in rotating it from the equilibrium through $$180^{\circ}$$ is :

Dipole has charge $$q = 4\mu C = 4 \times 10^{-6}$$ C and separation $$d = 18$$ cm $$= 0.18$$ m in a uniform electric field of magnitude $$E = 10^4$$ N/C.

The dipole moment is given by $$p = qd = 4 \times 10^{-6} \times 0.18 = 7.2 \times 10^{-7}$$ C m.

The work done in rotating the dipole from angle $$\theta_1$$ to angle $$\theta_2$$ in a uniform electric field is given by $$W = pE(\cos\theta_1 - \cos\theta_2)$$.

For rotation from $$0°$$ to $$180°$$, we have $$\cos 0° = 1$$ and $$\cos 180° = -1$$, so

$$W = pE(1-(-1)) = 2pE = 2 \times 7.2 \times 10^{-7} \times 10^4 = 14.4 \times 10^{-3}$$ J = 14.4 mJ.

The correct answer is Option 2: 14.4 mJ.