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

In summary, Coulomb's law only applies to point charges which are smaller than the distance between them.
  • #1
Ralphonsicus
47
0
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?
 
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  • #2
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 forcehttp://electron9.phys.utk.edu/phys136d/modules/m7/magnetic.htm.
 
  • #3
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.
 
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  • #4
Ralphonsicus said:
Am I wrong, or is there an equivalent that can work for magnets/big electric charges?
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
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
DaleSpam said:
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.

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
Hassan2 said:
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.
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
DaleSpam said:
Yes, he made his experiment with charged spheres. e time by then.

Thanks for the reply.

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
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
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?
 

1. What is Coulomb's Law?

Coulomb's Law is a fundamental principle in physics that describes the electrostatic interaction between two charged particles. It states that the magnitude of the electrostatic force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

2. Does Coulomb's Law only apply to point charges?

No, Coulomb's Law can also be applied to non-point charges, such as charged spheres or cylinders. However, it is important to note that the charges must be concentrated in a small enough area such that they can be treated as point charges for the equation to be accurate.

3. Can Coulomb's Law be used for both attractive and repulsive forces?

Yes, Coulomb's Law applies to both attractive and repulsive forces between charged particles. The direction of the force depends on the sign of the charges involved - like charges (positive-positive or negative-negative) will repel each other, while opposite charges (positive-negative) will attract.

4. How is Coulomb's Law different from Newton's Law of Universal Gravitation?

Coulomb's Law and Newton's Law of Universal Gravitation are similar in that they both describe the force between two objects, but they differ in the type of force being described. Coulomb's Law deals with electrostatic forces between charged particles, while Newton's Law of Universal Gravitation deals with the gravitational force between any two objects with mass.

5. What are the units for the constant in Coulomb's Law?

The constant in Coulomb's Law, also known as the Coulomb constant, has the units of Newton-meter squared per coulomb squared (N•m2/C2). This unit is used to maintain the proper units for the equation: Force (N) = (Coulomb constant) * (product of charges in coulombs) / (distance between charges in meters squared).

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