    Question

# Use Gauss's theorem to find the electric field due to a uniformly charged infinitely large plane thin sheet with surface charge density σ.

Open in App
Solution

## Consider an infinite plane which carries the uniform charge per unit area σ Let the plane coincides with the y−z plane.Let us draw a cylindrical gaussian surface, whose axis is normal to the plane, and which is cut in half by the plane.Let the cylinder run from x=−a to x=+a, and let its cross-sectional area be A. According to Gauss' law, 2E(a)A=σAϵ0,where E(a)=−E(−a) is the electric field strength at x=+a. Here, the left-hand side represents the electric flux out of the surface. The only contributions to this flux come from the flat surfaces at the two ends of the cylinder. The right-hand side represents the charge enclosed by the cylindrical surface, divided by ϵ0. It follows that E=σ2ϵ0.  Suggest Corrections  0      Similar questions  Related Videos   Gauss' Law Application - Infinite Sheet
PHYSICS
Watch in App  Explore more