1. Given data

• Charges: $-4\,\mu C$ and $+4\,\mu C$
• Positions: $(-9,0,0)\,cm$ and $(9,0,0)\,cm$
• Uniform electric field: $E=10^4\,N/C$

So the separation between the charges is $2a = 18\,cm = 0.18\,m$

2. Dipole moment

Magnitude of dipole moment is $p = q \times (\text{separation})$ $p = 4\times 10^{-6} \times 0.18$ $p = 7.2\times 10^{-7}\,C\,m$

3. Potential energy of a dipole in uniform electric field

The potential energy is $U = -pE\cos\theta$

• In stable equilibrium, dipole is aligned with the field, so $\theta=0$. $U_i = -pE$

• After rotation through $180^\circ$, $\theta=180^\circ$. $U_f = -pE\cos 180^\circ = +pE$

4. Work done in rotating from equilibrium through $180^\circ$

The work done by an external agent is the increase in potential energy: $W = U_f - U_i$ $W = pE - (-pE) = 2pE$

Now substitute: $W = 2 \times 7.2\times 10^{-7} \times 10^4$ $W = 14.4\times 10^{-3}\,J$ $W = 14.4\,mJ$

5. Option check

Thus the correct option is: $\boxed{D\; :\; 14.4\,mJ}$