# Electric dipole

## Homework Statement

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.

## Homework Equations

(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