Unlike Charges

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!

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.

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.

Last edited:
ZapperZ
Staff Emeritus