# Apply Gauss' law to find electric field around nonconducting plastic sheets

The question: Two very large, nonconducting plastic sheets, each 10.0 cm thick, carry uniform charge densities $\sigma_1$,$\sigma_2$,$\sigma_3$ and $\sigma_4$ on their surfaces, as shown in the following figure. These surface charge densities have the values $\sigma_1= -6.30$ $\mu \text{C}/m^2$ , $\sigma_2= 5.00$ $\mu \text{C}/m^2$, $\sigma_3= 2.10$ $\mu \text{C}/m^2$, and $\sigma_4= 4.00$ $\mu \text{C}/m^2$. Use Gauss's law to find the magnitude and direction of the electric field at the following points, far from the edges of these sheets.

Attempt: So, using Guass' law, I attempt to place the charge densities into a surface and use $E = \frac{\sigma}{2\epsilon_0}$, representing the sheets as infinite thin sheets.

For A, I have a surface encompassing every $\sigma$. $\sigma_1$ is negative, so it goes into the surface, and the other three are inside the surface and positive, so they are going from inside to outside the surface. Hence, for A, it should be $\frac{\sigma_2 + \sigma_3 + \sigma_4 - \sigma_1}{2\epsilon_0}$.

For B, I have a surface encompassing $\sigma_1, \sigma_2$ and one encompassing $\sigma_3, \sigma_4$. Well, again $\sigma_1$ goes into the surface, and the other three go out of their surfaces, so it would be the same answer as for A, but apparently this isn't right. I would use the same methodology for C, but it would be wrong. I don't understand how to approach this.

Edit: I have read solutions to this elsewhere, but they aren't in-depth enough and aren't satisfactory.

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When you consider $B$, pay attention to the direction of the fields from each surface charge. –  garyp Apr 11 at 16:56