An electric dipole of dipole moment is $$6.0 \times 10^{-6}$$ C m placed in a uniform electric field of $$1.5 \times 10^3$$ N C$$^{-1}$$ in such a way that dipole moment is along electric field. The work done in rotating dipole by 180° in this field will be ______ mJ.

We need to find the work done in rotating an electric dipole by 180° in a uniform electric field.

Formula for work done. The potential energy of a dipole in a uniform electric field is:

$$U = -pE\cos\theta$$

Work done in rotating from angle $$\theta_1$$ to $$\theta_2$$ is:

$$W = U_2 - U_1 = -pE\cos\theta_2 - (-pE\cos\theta_1) = pE(\cos\theta_1 - \cos\theta_2)$$

Initial and final angles. Initially, the dipole moment is along the electric field, so $$\theta_1 = 0°$$.

After rotation, $$\theta_2 = 180°$$.

Calculate the work done: $$W = pE(\cos 0° - \cos 180°) = pE(1 - (-1)) = 2pE$$

$$W = 2 \times 6.0 \times 10^{-6} \times 1.5 \times 10^3$$

$$= 2 \times 9.0 \times 10^{-3} = 18 \times 10^{-3} \text{ J} = 18 \text{ mJ}$$

The correct answer is 18 mJ.