Question: Dipole Moment from constant electric field
In  it is stated that the force per unit angle on a dipole system as illustrated in Fig.1 is
where . The text was also referring to torques, and it wasn’t clear to me if the result was the torque or the force. Derive the result to resolve any doubt (in retrospect dimensional analysis would also have worked).
Let’s put the electric field in the direction (), so that the potential acting on charge is given implicitly by
Our positions, and velocities are
Our kinetic energy is
For our potential energies we require the component of the position vectors, which are
Our potentials are
Our system Lagrangian, after dropping the constant reference potential that doesn’t effect the dynamics is
For this problem we had two equal masses and equal magnitude charges and
Putting these together, with , we have the result stated in the text
 E.A. Jackson. Equilibrium statistical mechanics. Dover Pubns, 2000.