Electric field between two metal plates

[toothpaste666]

Homework Statement

Two large, flat metal plates are separated by a distance that is very small compared to their height and width. The conductors are given equal but opposite uniform surface charge densities +σ and -σ. Ignore edge effects and use Gauss's law to show
a) the electric field between the plates
b) the electric field on on the outside of the plates on either side
c) how would my results be altered if the two plates were non conductors

Homework Equations

∫EdA = Q/ε

The Attempt at a Solution

a)

I made a imaginary cylinder where the surface A is perpendicular to the electric field
∫EdA = Q/ε
the Q enclosed is going to be the charge density times the area enclosed or σA
∫EdA = EA = σA/ε
the As cancel so
E = σ/ε

b) picture the same imaginary cylinder but fully extending all the way through and out the other side of both conductors now the Q on the right hand side of gauss's equation is the net sum of the enclosed charge or
Q = σA+ -σA = 0 so E = 0

c) this part I can't figure out. i need a hint to get started =[

 

[Philethan]

Hint:

1. What's the difference of conductor and non-conductor?

2. Ask yourself what the meaning of every step in (a) and (b) is.

You know there's something different in calculation when you are dealing with non-conductors.
However, you didn't find those "key condition" which is only fit with conductor.

 

[toothpaste666]

a non conductor will have no net charge?

 

[toothpaste666]

also since they are conductors does that mean the left surface of the positive plate will have a negative charge?

 

[Philethan]

1. For (a), you assume the electric field inside the plate is zero, and that's different in non-conductor case.

2. For (a), you assume the electric field outside the plate is perpendicular to the surface of metal plate, that's also different in non-conductor case.

also since they are conductors does that mean the left surface of the positive plate will have a negative charge?

I'm not sure why you think the left surface of the positive plate will have a negative charge in conductor case. But I think if there's still a negative charge in positive plate, then that means the positive plate is not in equilibrium state: static electricity equilibrium.

Suppose that there's a conductor and has positive charge on the one side and negative charge in the other side. Then, there must be some electric lines between the positive and negative charges( just like what you said). That means, those "hidden free electron" will be influenced by the electric field inside the conductor and starts moving until the electric field inside the conductor is zero, i.e. it's in static electricity equilibrium.