# Gauss's law in atomic scales

1. Mar 8, 2012

### Hassan2

Hi all,

Can we use Gauss's law to find the electric field near an electron, or is Gauss's law invalid in atomic scales? I ask this basic question because I know nothing about Quantum physics.

2. Mar 8, 2012

### issacnewton

It depends how close of electron you want to go. Acoording to Feynman ( Feynman Lectures Volume 2, page 5-7), the Coulomb's law fails at distances of $10^{-14}$ cm and less. Since validity of Gauss's law depends upon the validity of Coulomb's law, it means that Gauss's law also fails at this distance or below it. Feynman thinks there are two possible explanations for this. One, that Coulomb's law fails at such small distances. Or second, the electrons and protons are not point charges, perhaps either the electron or proton ,or both ,is some kind of a smear. Then he says that most physicists prefer to think that the charge of proton is smeared

Last edited: Mar 9, 2012
3. Mar 9, 2012

### Hassan2

Thanks issacnewton,

The scale I meant is about 10-10 m. Even at this distance , the electric field due to electrons and protons is extremely high. It seems practically impossible to take an electron away from the nucleus from with an applied electrostatic field.

4. Mar 9, 2012

### issacnewton

For that distance I think Gauss's law should work if what Mr Feynman is saying...