Where to place Gaussian surface

[henry3369]

Homework Statement

I'm trying to calculate the electric field through two oppositely charged plates with the same magnitude:
http://imgur.com/uXCQqtW

Homework Equations

Flux = ∫E⋅dA = Q_enclosed/ε₀

The Attempt at a Solution

I understand how the electric field is calculated using S1 and S4, but I have one question:
Why did the Gaussian surface have to contain a part of the plates? I ask this because if the surface was chosen to be between the plates, but not containing any parts of the plates, the electric field would be zero, since Q_enclosed is zero and the area, A, as well as ε are both constants. But, the electric field is definitely not zero between the plates.

 

[ehild]

Homework Statement

I'm trying to calculate the electric field through two oppositely charged plates with the same magnitude:
http://imgur.com/uXCQqtW

Homework Equations

Flux = ∫E⋅dA = Q_enclosed/ε₀

The Attempt at a Solution

I understand how the electric field is calculated using S1 and S4, but I have one question:
Why did the Gaussian surface have to contain a part of the plates? I ask this because if the surface was chosen to be between the plates, but not containing any parts of the plates, the electric field would be zero, since Q_enclosed is zero and the area, A, as well as ε are both constants. But, the electric field is definitely not zero between the plates.

The net flux is also zero if the flux across S1 and S4 (the opposite sides of the Gaussian surface) are of opposite signs and of equal magnitudes.

 

[henry3369]

The net flux is also zero if the flux across S1 and S4 (the opposite sides of the Gaussian surface) are of opposite signs and of equal magnitudes.

I'm not trying to find the net flux of S1 and S4. I'm using either S1 or S4 to find the electric field between the two charged plates. What I don't understand is why I can't use a Gaussian surface such as S1 and place it between the two plates without containing any parts of either plates to find the electric field. Because if it doesn't have any charge in it then E is zero because q_enclosed is zero. But there obviously is an electric field between the plates.

 

[phyzguy]

You can place the Gaussian surface anywhere you want. The fact that:

Net flux of E through the surface = Charge inside the surface / epsilon_0

is true for any closed surface. If you place the surface with both faces between the plates, then the charge inside the surface is zero, and the net flux of E through the surface is also zero. But this does not mean that E =0 between the plates! There is a flux of E into the surface on one side, and a flux of E out of the surface on the other side, so the net flux of E through the surface is zero. You have to keep track of the signs. If you place the surface so that one face is between the plates and one face is inside the conductor (like S4), the flux of E through the part inside the conductor is zero, so you only have to consider the face inside the plates. The trick in these problems is cleverly choosing your Gaussian surface in order to make the calculation easy.