How Does Gauss's Law Apply to Multiple Charged Sheets?

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Gauss's Law can be applied to determine the electric field created by multiple charged sheets by considering the contributions from each sheet separately. The electric field due to a single infinite sheet with surface charge density σ is given by E = σ/(2ε₀), but when multiple sheets are involved, the net electric field is the vector sum of the fields from each sheet. The confusion arises because the distances from the sheets affect the net field, requiring careful consideration of the direction and magnitude of each sheet's contribution. The correct approach involves calculating the electric field at point A by accounting for the effects of all charged sheets and their respective distances. Understanding how to apply Gauss's Law in this context is crucial for solving similar problems involving multiple charge distributions.
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Homework Statement



Two very large, nonconducting plastic sheets, each 10.0 cm thick, carry uniform charge densities \sigma1, \sigma2, \sigma3, & \sigma4 on their surfaces, as shown in the figure .

YF-22-30.jpg


These surface charge densities have the values \sigma1= -6.00E-6 C/m^2, \sigma2= +5.00E-6 C/m^2,\sigma3= +2.00E-6 C/m^2, and \sigma4= +4.00E-6 C/m^2.

A) Use Gauss's law to find the magnitude of the electric field at the point A, 5.00 cm from the left face of the left-hand sheet.



Homework Equations



Gauss's Law


The Attempt at a Solution



Well, at first this confused me because I'm pretty sure I remember that in Gauss's law, electric field depends only on the enclosed charge. But this problem gives me a lot of distances. So I guess the formula

E = \sigma/(2*\epsilon0 )

doesn't work. That's what I tried, anyway, and got the wrong answer. So, how do I approach a problem like this?
 
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Okay, I changed the problem.
 
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