# Is uniform electric field realistic?

1. Jul 20, 2014

### Axe199

I was learning about gauss's law and how to use to determine electric field, one of them is an infinite plane of continuous and uniform charge , eventually E= σ/2ε which means the E is not depend on the distance from the plane , does that mean anywhere i place a test charge above this plane it will experience the same force? can this happen in reality? or is it just a mathematical term?

2. Jul 20, 2014

Staff Emeritus
A uniform field for all space and all time is impossible, as it doesn't exist here and now. So it's an approximation. Like frictionless planes, stretchless ropes, massless pulleys, etc. That said, it cvan be a useful approximation.

3. Jul 20, 2014

### Axe199

what about metal they have a similar expression of the E , is that an approximation too? if yes , can we get the real number mathematically or just experimentally?

4. Jul 20, 2014

Staff Emeritus
I don't understand what you are saying.

5. Jul 20, 2014

### rcgldr

In the case of two oppositely charged plates (capacitor), the field between the two plates sufficiently inside the outer edges of the plates is a close approximation to a field of constant intensity.

6. Jul 20, 2014

### Axe199

i meant if we have a conductor , the field expression is σ/ε is this an approximation too?
if it's an approximation , is there a mathematical way to derive an accurate answer ? or the field is determined accurately at a certain point only by experiment?

7. Jul 20, 2014

### Matterwave

You mean for a finite sized charged plate? The field very near the center of the plate will be approximately the expression given. As you get farther from the plate and or closer to the edges the fields will become very different. The strengths as well as directions will change as well. But it's very hard to mathematically derive the fringe fields from first principles because the geometry is too complicated.

8. Jul 20, 2014

### Staff: Mentor

There are numerical methods for calculating the field (at least to some level of approximation) in a non-ideal configuration. If you have a specific configuration in mind, someone here might be able to tell you which is the most appropriate method for that configuration.

9. Jul 20, 2014

### ZetaOfThree

The electric field has magnitude $\frac{\sigma}{\epsilon_0}$ only at the surface of the conductor. It might change as you move away from the surface. This expression comes about from assuming that charge smoothly spreads out across the conductor's surface (and that Gauss's law is valid). Of course, charges come in clumps (electrons, etc.) so it's not smooth. So yes, it is an approximation... but a good one.

10. Jul 20, 2014

### Axe199

i have a certain setup in mind, for example , the electric field 1 m above the top of a van de graaff generator

11. Jul 20, 2014

### Axe199

electrons comes in clumps even in conductors like metals ?

12. Jul 20, 2014

### ZetaOfThree

Yeah. "Clump" is my colloquial term for "particle". Electrons are particles.

13. Jul 21, 2014

### Axe199

okay then , i thought clumps means something like lumps