Electricity and Magnetism Physics 208 Dr. Tatiana Erukhimova Lectures 10, 11

Gauss’s Law The total flux of electric field out of any closed surface is equal to the charge contained inside the surface divided by .

The flux of

Electric flux through a sphere A positive point charge q=3.0 C is surrounded by a sphere with radius 0.2 m centered on the charge. Find the electric flux through the sphere due to this charge.

S Definition of a solid angle does not depend on radius The largest Then

Proof of Gauss’s Law

Electric field of a single fixed charge Chasing the tail: Electric field of a single fixed charge

Conductors and insulators Charges reside at the surface of the conductor + + + + + + + + Conductor + + E=0 + + + + +

Solid conducting sphere with charge Q V r A r

Electric field of a ball of charge Q Electric field outside of a charged sphere is exactly the same as the electric field produced by a point charge, located at the center of the sphere, with charge equal to the total charge on the sphere.

Have a great day! Hw: All Chapters 4-5 problems and exercises Reading: Chapter 5