# What are point charges?Why we use point charges for coulomb's law?

1. Jul 17, 2013

### kashan123999

1. The problem statement, all variables and given/known data

What is a point charge? and what is the purpose of it when the definition of coulomb's law says,"force b/w TWO POINT CHARGES is directly proportional to their magnitude,and inverse to the square of their distance....."...I mean what is the use of it,why only point charges??

2. Relevant equations

F=kq1q1/r(sq.)

3. The attempt at a solution

Ok as far as I can get it,point charge is a charge which is very very small,but I still couldn't get the idea of "Point" charge please explain and also why we use them?

2. Jul 17, 2013

### Simon Bridge

Did you do any geometry in your math classes?
Is a point merely "very small"?

To see why we use them, imagine a charged sphere with a fixed radius R ... for r>R, what is the electric field?
(This may be uniformly charged or a charged shell.) Have you met Gauss' Law yet?

3. Jul 17, 2013

### kashan123999

so complex you are,No haven't met it,it is quite far still at least in our coursebook curricula...

4. Jul 17, 2013

### Simon Bridge

I was just asking so I could help - what about the other questions?

Did you do any geometry in your math classes?
Is a point merely "very small"?

To see why we use them, imagine a charged sphere with a fixed radius R ... for r>R, what is the electric field?

5. Jul 17, 2013

### kashan123999

I haven't read about electric field yet,point is just a point,not small...it is a geometrical point...so are you saying that the point charge is actually a geometrical point?

6. Jul 17, 2013

### phinds

One thing he is saying that if you do NOT treat a point charge AS a point charge (yes, a geometrical point with no dimensions) then the math gets more complex than you even want to THINK about.

7. Jul 17, 2013

### ehild

We use simplified models in Physics. It is impossible to describe reality in full detail. And it is not needed in many cases. You can measure things with some accuracy, and details which do not effect a measurable quantity more then the measurement error, can be safely ignored. So we use the concept point mass and point charge, as it is easy to calculate with points instead of extended objects. They mean small (usually spherical) objects whose radii is much-much smaller than the distances in the problem. Both the Sun and Earth can be considered as point masses when you describe the orbit of Earth around the sun. A proton can be considered a point charge when you calculate the force it exerts on the electron orbiting around it in a hydrogen atom. The shape of a stone you throw, slightly will influence how far it reaches, but only in a small amount. If you do not measure with very high precision, it also can be considered point-like.
Coulomb's Law refers to the force between point charges. Extended charged objects can be considered as a lot of point-like charges arranged in some way, and the force between the objects is the resultant of the forces between pairs of those point charges.

ehild

8. Jul 17, 2013

### WannabeNewton

With regards to the math, you do treat the object as a literal point and you'll notice that this comes with associated geometric singularities (e.g. at $r = 0$). Classically there are mathematical issues with the notion of a point charge. The resolution however is quite deep and beyond the scope of introductory physics I'm afraid but your question is a very, very nice one.

Last edited: Jul 17, 2013
9. Jul 17, 2013