What happens when two unlike charges get extremely close together?

[phisci]

Hi everyone,

I was wondering if 2 unlike charges are placed a certain distance d apart, they will attract and move towards each other and the attractive force is given by Coulomb's kq1q2/r^2. Since r cannot be equals to zero as it would imply that the 2 charges exist as the same point in space, there has to be a closest approach of some kind. What then happens when distance r between these 2 charges are extremely close to 0?? Correct me if my reasoning is flawed. Thanks!

 

[JaredJames]

Well the limit would be > 0. Anything above zero.

You're trying to think of it as if you're assigning a radius to the charge itself. That is not what a point charge is.

http://en.wikipedia.org/wiki/Point_particle

A point particle (ideal particle[1] or point-like particle, often spelled pointlike particle) is an idealized object heavily used in physics. Its defining feature is that it lacks spatial extension: being zero-dimensional, it does not take up space.

Emphasis mine.

http://dictionary.reference.com/browse/point+charge

an electric charge considered to exist at a single point, and thus having neither area nor volume.

Because they don't have any dimensions, r has to be > zero but it can get as close as it likes.

 

[Rap]

In reality, the physics changes as the two point particles get very close. An electron and and a positron is a real-world example. At some point in their approach, the two will annihilate and produce two photons, usually.

Classically there is a problem. As the two particles approach each other, they will accelerate to infinite speed, producing an infinite energy. Even relativistically, they will approach the speed of light producing an infinite energy.

 

[mrspeedybob]

To oversimplify... Electron + Proton = Neutron + Neutrino

For more detail... http://en.wikipedia.org/wiki/Electron_capture

Edited to correct incompleteness pointed out by ZapperZ

 

[ZapperZ]

To oversimplify... Electron + Proton = Neutron.

For more detail... http://en.wikipedia.org/wiki/Electron_capture

Unfortunately, this is TOO over simplified that it is wrong. As is clearly stated even in that Wikipedia entry, electron + proton is NOT equal to neutron. Without a neutrino involved, it violates at least one conservation law.

Zz.