Using the general expression for the electric field of a dipole, estabilish a simplified expression for the electric field at a point along the x-axis produced by a dipole (p1) at the origin in the z direction.
Use this to find the energy of a second dipole p2 placed at a point x in 3 cases when i) p2 is parallel to p1 ii) they are perpendicular iii) they are anti-parallel. Then for each case find the force on p2 and the work done by an external agent bringing p2 towards x.
(simplified, although they should be written as vector integrals)
Dipole moment: p = qd
Field: E = kQ/r²
Force: F = EQ = kQq/r² = kpd/r²
Energy: U = kQ/r
(k= Coulombs constant, Q= source, q=test charge, r=distance between charges)
The Attempt at a Solution
For the first part, the dipole moment p at the origin would have charge q (point of the x axis) and the distance d (between that point and the origin). Then d = r (between reference point) so E = kpd/r² = kpd/r
So would the energy just be the field integrated along the distance r. Would the orientation of p2 would just change the sign for the energy: positive if they're parallel, zero if perpendicular and negative if antiparallel? Im still kind of confused between work, energy and potential in electrostatic fields