B Electric Field Created by 2 Infinite Plates

[Heisenberg7]

Today, I watched a video about electric field created by an infinite plate by Khan Academy. They were talking about the clever application of the Gauss's law in this case (the cylinder method), so I wondered if I could apply the same thing but to 2 plates. For example, let's say that the plates are parallel. In this case the electric field created by one plate is $E = \frac {\sigma}{2\epsilon_o}$. Since electric field is a vector quantity we can vectorially add up the electric field created by both plates. Between the plates the electric field created by one plate is opposite and equal to the electric field created by the other, thus if we vectorially add them up, we get 0. But on the left and right side, it's different. They have the same direction and magnitude at each point in space, thus the electric field at any point is $E = \frac {\sigma}{\epsilon_o}$. Is this the correct way to think about this problem? (both plates have the same charge $q$)

 

[Orodruin]

Yes, electric fields generated from different sources add up to a superposition of the individual contributions. However, note that this is a result of the linearity of the governing differential equation, ie Gauss’ law or ultimately Maxwell’s equations. It does not follow solely from being a vector field.