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This is a matter of limits. If you are measuring the electric field at a point that is a distance off of an infinite sheet of charge the direction of the electric field will be perpendicular to the sheet due to the symmetry of the situation. We can think of the radius as the distance between a point on the sheet and the normal line to the sheet that passes through the point where the electric field is being considered. If we look at the addition to the electric field from the charge on the sheet as this radius approaches infinity the component of the electric field in the direction of the net electric field will approach 0.

P.S. Drawing a diagram of the situation with arrows denoting the directions of force from different parts of the sheet can be very helpful in understanding.

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no gauss low is only applicable for closed paths. a plane sheet is not a closed path. for applying gauss law the charge must be inside the closed loop or path... ========================== I'll say "yes". Gauss' law says that the electric flux through a closed surface is proportional to the amount of charge inside the closed surface. The shape of the surface doesn't matter, and the shape of the charge distribution inside it doesn't matter either. If a closed surface encloses a part of a sheet of charge, then the flux through the surface is proportional to the amount of charge that's on the part of the sheet inside the surface. That doesn't bother me at all.


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What is the application of Gauss's Law in determining the electric field produced by an infinite sheet of charge?

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