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If we have two parallel charged plates, equal and opposite in charge:

What is the flux felt on a Gaussian surface between them? surely it sum to 0 as each amount of flux will enter and then leave? This must be wrong as it would mean the field between the two plates is also zero?

Let me know what i'm missing, thanks!

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  • $\begingroup$ related: physics.stackexchange.com/questions/109803/…. The person asking that questions makes the same mistake of concluding that the electric field is zero when its divergence is zero. $\endgroup$ – Brian Moths Apr 29 '14 at 13:25
  • $\begingroup$ The flux in Gauss' law is the flux that exists a closed surface between them. If, as you say, what enters the closed surface, leaves it eventually, then implies that the total exiting flux is zero as the entering flux contributes negatively to the total leaving electric field. $\endgroup$ – gatsu Apr 29 '14 at 13:30
  • $\begingroup$ I'm still not sure I understand. I assume my mistake is in using Flux=electric field * area, and then deducing that if flux is zero that electric field must also be? $\endgroup$ – Jbarrell Apr 29 '14 at 13:40
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Note that area is a vector. When you take a,say, cubical box, Electric Field acrsos both opposite faces is same. But areas are $\vec {A}, -\vec{A}$. And the flux is :

$$\vec{E}.\vec{A}+\vec{E}.-\vec{A}=0$$

Flux across rest faces is zero as area is perpendicular to electric field

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