A point charge q is situated a large distance r from a neutral atom of polarizability α. Find the force of attraction between them.

Solution 4P

Step 1 of 5:

Consider a point charge q and a neutral atom is separated by a distance r. The polarizability of the atom is α. This is the ability of the atom to form a dipole. We are going to force of attraction between the atom and the point charge. Before that, we should find the electric field due to the dipole formed by the point charge and the atom.

Step 2 of 5:

The electric field produced by the point charge q is given by

The induced dipole moment due to the field

Substituting (1) in (2)

Step 3 of 5:

Now the point charge and the atom become a dipole producing an electric field Edip. The expression is given by

Where are unit vectors. The point charge and the atom are in the same line and the angle (θ) between them is 180°. Therefore the above equation becomes