# Coulomb's Law vs. Gauss's Law Paradox

1. Jan 19, 2008

### breez

From Coulomb's law, as the distance between a charged particle and another charged particle approaches zero, the electrostatic force between the two particles approaches infinite.

However, according to Gauss's Law, we know that for a uniformly charged sphere or spherical shell, the charge effectively acts as if the entire charge of the sphere were concentrated at its center. So when a charged particle's distance from the surface of the sphere approaches zero, the electrostatic force between them no longer approaches infinite. I am confused...seems the forces are all acting one way (pushing particle toward the sphere if oppositely charged and away if same charges).

2. Jan 19, 2008

### tim_lou

the problem with your logic is the idea of point charges. In the case of spherical shell, the charge at each SINGLE point is zero. The charge for the spherical shell is described by a charge density, and for a vanishing surface area, the charge is zero in a way such that the infinity in Coulomb's law is canceled. Indeed, if you assume that each point on the shell has a charge, let's say q, the total charge on the shell would be infinite, since there are infinitely many points on the shell.