(Solution) - An electric dipole consists of two charges q and q -(2025 Original AI-Free Solution)

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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 (dEx/dx)pi.