Required math: calculus
Required physics: electrostatics
Reference: Griffiths, David J. (2007) Introduction to Electrodynamics, 3rd Edition; Prentice Hall – Chapter 4, Post 4.
In an earlier post, we saw that placing a neutral atom in an external field induces a dipole moment where for small fields the experimentally determined relation is
where is the atomic polarizability.
If this external field is due to a point charge at a distance from the atom then the field at the atom due to the charge is
The induced dipole moment is therefore
We’ve seen that the electric field due to a dipole is (in spherical coordinates):
The field from the dipole induced by the point charge is therefore
where points along the line from the atom to the point charge. The point charge is thus located at so the force on the charge due to the dipole is