# Parallel plate capacitor

How does a parallel plate capacitor emit a constant electric field between its plates? Isn't the electric field governed by an inverse square law? Then what would happen if I put a charged particle between the plates - would it experience the same force everywhere throughout the volume between the plates?

In my book it is given that outside the parallel plate capacitor the electric field is zero, but how does this come about? The electric field has a inverse square dependence as to my knowledge so since the plates are at a distance away from each another the electric field at a point would not be negated out to $0$.

We are given the formula that $E=\frac{\sigma}{2\epsilon_0}$ for a infinitely long sheet so my question to that is: What is the charge density and its relation with $E$ and $r$ where $E$ is the electric field and $r$ is the distance from the sheet to a point?

• Regarding your 2nd sentence, the electric field of a point charge is inverse square law but not for other collections or distributions of charge. For example, the electric field an arbitrarily long line of charge through the origin is proportional to $r^{-1}$ rather than $r^{-2}$. – Alfred Centauri Oct 4 '14 at 12:30
• w8 how is it to r^-1 and not r^-2 .. does this have something to do with potential field or something? – Christopher Pinto Oct 4 '14 at 12:36
• This is elementary EM and the derivation is of this result is ubiquitous, e.g., hyperphysics.phy-astr.gsu.edu/hbase/electric/elelin.html What specifically is not clear in the derivation of the electric field of the infinite line charge? – Alfred Centauri Oct 4 '14 at 13:22
• I'm not clear on your 3rd paragraph. In engineering we use $\sigma$ for the conductivity of a material. Are you using it for charge density? – The Photon Oct 4 '14 at 16:51

## 1 Answer

How does a parallel plate capacitor emit a constant electric field between its plates?

Remember that the parallel plate capacitor is an idealization. The rules for it really only apply in the limit as the transverse dimensions of the plates go to infinity.

in my book it is given that outside the parallel plate capacitor the electric field is 0, but how come?

If I recall correctly, this is proved using Gauss's law and symmetry arguments. Gauss's law is also used to show the uniformity of the field between the plates.

Isn't electric field a inverse square law?

The electric field falls as the inverse square of the distance, when you are "far away" from all the charges in the system. When you are considering a point between the plates of a parallel-plate capacitor, any change in position away from one plate (and one region of charge) moves you nearer to the other plate (and other charges), so we can't consider these points to be "far" from the charges.