# Calculating Electromagnetic Force at 0 Distance?

1. Apr 18, 2014

### one_raven

If you'll allow me to disregard the effects of Strong Interaction, how would I calculate the Electromagnetic Force between two oppositely charged point particles that are in contact with one another?

Let's assume two particles with opposite Elementary Charges: 1.60218E-19 and -1.60218E-19 and start with an assumption of a distance of 1fm...

(Please forgive my pathetic excuse for scientific notation)

F = q1*q2 / (4πεo * r²)

That gives us: 1.60218E * -1.60218E / (1.11265E-10*1E-15^2) = -231
This means, if I understand it correctly, separating the particles from this distance would require 231 Newtons of force. Right?

First: As distance approaches zero, force approaches infinity, but it can never be zero in this equation.
If I'm not mistaken, the distance should be measured from center of mass to center of mass, so it never could be truly zero for massive particles. Given that, my assumption is that the distance for two identical spheres should be the radius.
I get that, but where it loses me is when people say that point particles have no shape, because they exist as a point - therefore have no "size".
Do electrons have a physical size, and that's why the distance could never be zero?

Second: If we're talking about two particles touching, shouldn't the Vacuum Permittivity (Dielectric Constant - or whatever term you want to use) be discarded?
If so, how would we do that? What would the resulting equation look like?
If not, why not?

Thanks

2. Apr 18, 2014

### dauto

No, electrons don't have a size. Proton's on the other hand do because protons are NOT fundamental particles. The solution for this problem has to do with the fact that due to Heisenberg's Uncertainty Principle a particle cannot be localized to an exact point so it doesn't make sense to try and find the force and/or energy related to two particles at exactly same coordinate.

3. Apr 18, 2014

### one_raven

OK.
Let's take two other hypothetical particles, then.
Again, disregard the Strong Interaction, so they can touch...
Wouldn't them touching negate the effect of the Dielectric Constant, since there is no space between them? How could that be reflected in the calculation?

4. Apr 18, 2014

### Einj

The Heisenberg principle is true for every two kind of particles. The closer the particles the greater their momentum. Therefore you cannot really make the two particles touch because they would escape from each other.

Moreover, according to QED, the closer you are to the electron the greater is its charge, since you are deeply into the virtual vacuum polarization.

5. Apr 18, 2014

### Drakkith

Staff Emeritus
You are trying to use classical physics where Quantum Mechanical rules are needed. And this is much, MUCH more complicated. They can't even "touch" in the classical sense because fundamental particles are point-like and have no volume. Instead, they are represented by a wave packet that determines the probability of finding them in certain positions and states.