A small electric dipole is made of charges of $+4.0\ \text{nC}$ and $-4.0\ \text{nC}$, held $1.0\ \text{mm}$ apart. Its dipole moment $\vec p$ points from the negative charge to the positive one. A point charge of $+6.0\ \text{nC}$ is held $20\ \text{cm}$ from the centre of the dipole, on the line through the centre at right angles to $\vec p$, as in the figure. The size of the dipole is tiny compared with this distance. Both are in empty space. Take $\dfrac{1}{4\pi\varepsilon_0} = 9.0 \times 10^{9}\ \text{N m}^2\,\text{C}^{-2}$. What force does the point charge exert on the dipole?

Fig. 1: A small dipole lies on a horizontal line: a charge of minus 4.0 nanocoulombs on the left and plus 4.0 nanocoulombs on the right, 1.0 mm apart, with an arrow p pointing from the negative to the positive charge. A point charge of plus 6.0 nanocoulombs sits 20 cm straight above the centre of the dipole, on a dashed line at right angles to p. The dipole is drawn larger than to scale.