# Why r R is electric field of a point charge?

1. Feb 11, 2012

### livewire5

I am not sure why or how the distance away from a charged conductor, r, is greater than the radius of that charged conductor or surface, R, then the electric field is that of a point charge.. if r>>R then we are far from conductor. if r<<R then we are close to the conductor..

these are things textbook says but I dont know why this is can someone please explain why the above is true?

2. Feb 11, 2012

### Staff: Mentor

If you're far enough away from some finite distribution of charge, it looks like a point charge.

3. Feb 11, 2012

### Staff: Mentor

If r << R, surely you are inside the conductor!

4. Feb 11, 2012

### livewire5

but what if you have an infinite charged plane or a disk of charge it would be aligned up in x-y axis and your z axis would be the r and surely the Radius R would just mean the distance z is which isnt inside that charged plane......what you are saying works for sphere of charge or other 3d charged planes is my thought

5. Feb 12, 2012

### BruceW

eh? Your last post confused me, but I'll try to answer the original question: When you've got a charged object of some finite size, then you can imagine that when you go very far away from it, the vector from you to any point inside the charged object is almost exactly the same, so the electric field acts almost as if the object was all concentrated at the same point. But if the charged object is an infinite plane, then no matter how far away you go, it is still the same shape, so in this case, it does not approximate a point charge. This is what Doc Al meant when he said finite distribution of charge.

6. Feb 12, 2012

### ZapperZ

Staff Emeritus
First things first. Have you solved the electric field these types of charge distribution using Gauss's Law? You have neglected in describing what you know and what you have done. I have no way of knowing the starting point in explaining anything that you have asked.

Zz.

7. Feb 12, 2012

### Mindscrape

If you have an infinite plane, obviously it looks infinite whether you are really close or really far away. You can, however, approximate fields with r=R+Rc, where Rc<<R, as infinite planes, cylinders, etc. This works because if you get really close to the surface it can look approximately infinite.

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