### In an arbitrary field

The easiest way to get the force over a dipole is to consider it as the limit of two oppositely charged monopoles that are closely spaced. If the dipole has moment and is at position , it can be considered as the limit of two monopoles, one with charge at position and the other with charge at position , when goes to zero.

If we consider the finite size dipole immersed in a (let’s say magnetic) field , the total force will be

.

We can get the force for the infinitesimal dipole by taking the limit when goes to zero

,

where is the (tensor) derivative of the magnetic field.

### Between two antialigned dipoles

The general field of a magnetic dipole of moment at position is

.

If we assume we have one dipole at with its moment and the other at with its moment , we get a field at of

.

By symmetry, we are only interested in the x-component of the x-derivative of the field,

.

And the force on the dipole at will be

,

a repulsive force as expected of antialigned dipoles.