# What is Coulomb potential and energy?

1. Aug 16, 2011

### quietrain

is it just potential and potential energy?

but if so, why is it given as

V(r) = - Ze2 / 4πεr ?
and
E = Z2e2 / 4πεr

i am having trouble understanding how come for potential V, Q = Ze2

while

for E, Q2 = Z2e2

thanks!

2. Aug 16, 2011

### chrisbaird

If E is meant to denote the classical electrostatic field and V the classical electrostatic potential, then your equations look all wrong. Where did you get them?

The term "Coulomb potential" is essentially used to mean the potential that gives rise to a classical electrostatic force (quantum effects can be neglected). Van der Waals force potentials, covalent bond potentials, quantum wells, etc. are all electromagnetic potentials but are quantum in nature.

3. Aug 16, 2011

### quietrain

i got them off my notes, but they may be wrong

so is it right that charge Q = Ze?

so electric potential energy = kQQ/R = k(Ze)2/R ?

Ze is bascially the charge of the nucleus right? number of proton mulitply by electron charge e?

also, so the term "coulomb" refers to classical electrodynamics mainly?

4. Aug 16, 2011

### chrisbaird

Yes, if you are neglecting screening and quantum effects, then the total charge of a mass it the number of elementary charges (protons) times the charge of one element.

I think I see the problem. Coulomb Potential energy U = kQ1Q2/R where Q1 is the charge of the one particle and Q2 is the charge of the other. If you are treating a one-electron atom classically, then for the electron Q1 = -e and for the protons, Q2 = +Ze so that:

U = k(-e)(Ze)/R = - k Ze2/R

Yes
Yes

5. Aug 17, 2011

### quietrain

ah i see... but why is an atom "one-electron" classically?

6. Aug 17, 2011

### chrisbaird

When you have an atom with more than one electron, the quantum effects become so strong that using a classical approach is rendered essentially useless. If you are going to use Coulomb's law to describe an atom (already a shaky proposition), it's best to keep to one-electron atoms. Even with the help of quantum theory, deriving the potential of a multi-electron atom is nontrivial. Sadly, most of the atoms we encounter in every day life are multi-electron, so the clean one-electron pictures are not entirely useful.

7. Aug 18, 2011

### quietrain

i see thank you very much