A small neutral metal sphere is placed at a large distance from a point charge. By what factor would the Coulomb force between the charge and the sphere change if the distance between them is doubled?
Adapted from Kvant, 2001
Solution:
When a neutral conducting sphere is placed in a uniform electric field, the charge is redistributed on its surface to give it a dipole moment “p” which is proportional to the strength of the original uniform field, and which is parallel to the original field.
The force of attraction between the particle and the dipole is equal to the product of the particle’s charge “q” and the dipole’s electric field strength at the particle’s location.
The dipole’s field strength is proportional to the dipole moment and inversely proportional to the third power of distance from the dipole.
In this case, the original electric field is produced by the charged...
