Gauss's Law

Example: Plane of Charge

( or Sheet of Charge )

Consider an infinite sheet or plane of charge with charge density

Now for our "Gaussian surface" -- our surface of integration -- use a cylinder with its axis perpendicular to the plane. By symmetry, the electric field must be perpendicular to the plane. Therefore the flux through our surface is just the flux through the ends of the cylinder. There is no flux through the "cylindrical side" of the surface since the electric field there is parallel to the surface. That is,

= E (2 A)

= Q /

Q = A /

E (2 A) = A /

2 E = /

E = / 2



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(c) Doug Davis, 2002; all rights reserved