Unit 1 Day 11: Applications of Gauss’s Law Spherical Conducting Shell A Long Uniform Line of Charge An Infinitely Large, Thin Plane of Charge Experimental Basis of Gauss’s Law

A Thin Spherical Conducting Shell of Radius r 0 Charge is uniformly distributed E-Field is symmetric at all points Outside the shell the E-Field penetrates surface A 1 perpendicular to the surface Inside the shell (r < r 0 ), the E-Field does not penetrate A 2, and E=0, because Q=0

Solid Sphere of Charge Outside the Sphere (r > r 0 ) Inside the Sphere (r < r 0 ) but Q encl is not the total charge Q but a percentage of it, by volume:

Solid Sphere of Charge

A Uniform Line of Charge A very long straight wire, possessing a uniform charge density: The Gaussian Surface is a cylinder where the E- Field is perpendicular at all points

An Infinitely Large, Thin, Plane of Charge Assume a uniform charge density Choose a Gaussian Surface as a small closed cylinder whose axis is perpendicular to the plane The E-Field is directed perpendicular to the plane on both sides & uniform over the end cap of the cylinder of area A

Experimental Basis of Gauss’s & Coulomb’s Laws Gauss’s Law requires that any net charge must reside on the surface of a conductor The charge will flow to the outside Test the outside of the can for charge Test the ball after touching inside of can & withdrawn: charge will be zero