Infinite Sheet of Charge : Electrostatics

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Joined Jun 6, 2008

I am working on a homework problem from electrostatics.

From Gauss's law, the electric field intensity due to an "infinite" planar charge distribution is given by E = σ/(2ε). Assuming a plane on the z-axis, we know that a field magnitude given by E = σ/ε comes out of each of the sides of the charge sheet. Well, my homework question gives three such "infinite" sheets of charge,

1) σ1 = -10nC/m^2 at z = 5
2) σ2 = 5nC/m^2 at z = 1
3) σ3 = 12nC/m^2 at z = -7,

and asks for the electric field at (0,0,0). Do I sum up the electric field contributions from all the charge sheets?

Specifically, for this problem, at (0,0,0) is the electric field equal to

((-σ1-σ2+σ3)/ε)k-hat ??