Coulomb's law states that the force of attraction or repulsion between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them, acting along the line joining them. Mathematically, F = k q1 q2 / r^2, where k = 1/(4 pi epsilon0) = 9 x 10^9 N m^2 C^-2 in free space.

F = k q1 q2 / r^2

The electric field intensity at a point is the force experienced by a unit positive test charge placed at that point. It is a vector quantity given by E = F/q0, where q0 is the small positive test charge. Its SI unit is newton per coulomb (N/C) or equivalently volt per metre (V/m).

E = F/q0

When a dipole of moment p is placed in a uniform electric field E at an angle theta, the two charges experience equal and opposite forces qE, forming a couple. The magnitude of the torque = force x perpendicular distance = qE x (2a sin theta) = (q x 2a) E sin theta = pE sin theta. In vector form, torque = p x E. The torque tends to align the dipole with the field.

torque = pE sin theta = p x E