Electric field from a positive and negative plate pair

[annamal]

Homework Statement

Two large conducting plates carry equal and opposite charges, with a surface charge density as shown in image. The separation between the plates is d. What is the
electric field between the plates?

Relevant Equations

$\vec E = \frac{\sigma}{\epsilon_0}$

I am confused with the solution. It says $\vec E = \frac{\sigma}{\epsilon_0}$. Shouldn't E = $2*\vec E = 2*\frac{\sigma}{\epsilon_0}$? Electric field of the positive plate and electric field of the negative plate.

 

[kuruman]

I am confused with the solution. It says $\vec E = \frac{\sigma}{\epsilon_0}$. Shouldn't E = $2*\vec E = 2*\frac{\sigma}{\epsilon_0}$?

It should not. Use a pillbox Gaussian surface with one flat face inside the conductor and the other flat face in the vacuum to see why and become unconfused.

 

[Delta2]

Well if you mean that the total E-field should be double of that of the one plate, yes that is true but the field of one plate is $E=\frac{\sigma}{2\epsilon_0}$. So the total field is $$2\frac{\sigma}{2\epsilon_0}=\frac{\sigma}{\epsilon_0}$$