An electric dipole consists of two charges +q and –q separated by a very small distance 2a. Its center is on the x axis at x = x₁, and it points along the x axis in the positive x direction. The dipole is in a nonuniform electric field, which is also in the x direction, given by E = Cxi, where C is a constant.

(a) Find the force on the positive charge and that on the negative charge, and show that the net force on the dipole is Cpi.

(b) Show that, in general, if a dipole of moment p lies along the x axis in an electric field in the x direction, the net force on the dipole is given approximately by (dE_x/dx)pi.