# Does Coulomb's Law apply to more than point charges?

1. Feb 24, 2012

### Ralphonsicus

I read an article on Coulomb's law which read, ''Coulomb's law only applies to point charges'' (or something along those lines). Am I wrong, or is there an equivalent that can work for magnets/big electric charges?

2. Feb 24, 2012

### rktpro

IMO, which doesn't actually counts, I think coulomb's law in applicable only to charges which are smaller than the distance between them.
And Coulomb's law is there in electrostatics. You might read more about magnetic field and force here.

3. Feb 24, 2012

### Hassan2

Yes, Coulomb's law is basically defined for point charges. For large bodies, one needs to integrate the partial forces exerted on differential volumes of the bodies.

However,for uniformly charged spheres or spherical shells ( due to symmetry ) , Coulomb's law can be readily used by inserting the distance between the centers of the sphere in the formula. This may be proved by integration but it seems difficult to me. I have a simple and interesting proof for it based on Newton's third law though.

Last edited: Feb 25, 2012
4. Feb 25, 2012

### Staff: Mentor

You are correct, Coulomb's law only works for point charges. If you have a spherically symmetric charge then you can use Newton's shell theorem in conjunction with Coulomb's law to get the force. For more general distributions of charge you need to use Gauss' law. Coulomb's law is essentially Gauss' law evaluated for a point charge.

5. Feb 25, 2012

### Staff: Mentor

And of course Gauss's Law, while always true, is usable in practice only for certain very symmetrical shapes of charge configurations. For other shapes (e.g. a cylindrical rod of finlte length) you have to integrate Coulomb's Law after dividing up the shape into a lot of infinitesimally small sections which each act like a point charge, at different distances from the point at which you want the field.

A few days ago I had to work out the electric field at a distance z above the center of a thin square sheet of side a, with uniform charge density. I ended up with about three pages of math, setting up and solving a double integral.

6. Feb 25, 2012

### Hassan2

I wonder if Coulomb made his experiment with uniformly charged spheres. And also if he knew about the Newton's shell theorem. Otherwise he couldn't postulate the law precisely.

7. Feb 25, 2012

### Staff: Mentor

Yes, he made his experiment with charged spheres. I am pretty sure that he knew about Newton's shell theorem since it had been in existence for quite some time by then.

8. Feb 25, 2012

### Hassan2

To my knowledge,Van de graff generators charge conducting spheres rather than dielectric ones. When two conductive spheres are placed near together, the surface charge distribution is not uniform anymore. Am I wrong?

It's not that easy to charge dielectric spheres uniformly or perhaps there are effective ways to do this which I'm not aware of.

Thanks again.

9. Feb 26, 2012

### Staff: Mentor

I am not aware of the details of the charged spheres. I am sure if you looked you could find Coulomb's description of the experiment. Given the accuracy of measuring forces I doubt that the details of the charge distribution were the dominant source of error in his experiment.

10. May 4, 2012

### Rburto

Hypothetical question:

If two oppositely charged point charges have a distance between them of 0 m, how could they be separated; Coulomb's Law would indicate that the electric force between the charges would be an infinite amount of Newtons?