# Electric field in a parallel plate capacitor

#### Skyrim

The Electric Field in a parallel plate capacitor is approximately constant between the plates of the capacitor. Why is this so? I imagine it is only true if the distance between the capacitor is small compared to the area of the plates or it may just be the opposite of that. Prove it mathematically if you can, using Gauss' Law where applicable.

I have tried understanding it in a similar way to the reason why 'g' is a constant near the Earth surface's but I can't quite form of the mathematics behind it for the case of electrical capacitors.

~Sky

#### topsquark

Forum Staff
The Electric Field in a parallel plate capacitor is approximately constant between the plates of the capacitor. Why is this so? I imagine it is only true if the distance between the capacitor is small compared to the area of the plates or it may just be the opposite of that. Prove it mathematically if you can, using Gauss' Law where applicable.

I have tried understanding it in a similar way to the reason why 'g' is a constant near the Earth surface's but I can't quite form of the mathematics behind it for the case of electrical capacitors.

~Sky
Have you tried to solve the problem using Gauss' Law? The only other way that I can think to approach this problem is to consider the electric potential between the two plates: it is a linear function of the position of measurement between the two plates. So E has to be constant.

Unfortunately that g is almost a constant has no bearing on this problem. Sorry!

-Dan

Edit: Well, maybe I'm being a bit hasty. Conceptually the electric field due to an infinite plane must be constant. You can easily compute this using Gauss' Law, but it should be fairly obvious due to the symmetry of the problem. So if you put two "infinite" planes together, the E field between them would just be the sum of the electric field of each, and so that will be constant also.

And yes, if the world were flat, then the g analogy would hold as well, for similar reasons to the constant E field. I was wrong about that.