Gauss’ Law and Applications
Today’s Topics
Clicker Question
Clicker Answer
Dipole Field Lines in 3D
Velocity Field for a Steady Source in 3D
Total Flow through any Surface
Gauss’s Law
What about a Closed Surface that Doesn’t Include the Charge?
What about More than One Charge?
Gauss’ Law
Spherical Symmetry
Field Inside a Hollow Shell of Charge
Field Outside a Solid Sphere of Charge
Clicker Question
Clicker Answer
Clicker Question
Field from a Line of Charge
Clicker Question
Coaxial Cable Question
Uniform Sheet of Charge
Charge on Surface of a Conductor

Spherical Symmetry

First, a uniform spherical shell, radius r0, of positive charge.
The perfect spherical symmetry means the electric field outside, at a distance r from the center, must point radially outwards. (rotating the sphere doesn’t change anything, but would change a field pointing any other way.)