GAUSS' LAW

I. For an electric field E the flux is measured by the number of field lines that cut through a surface.









II. Gauss' Law says that the flux through a closed surface is proportional to the total charge inside the closed surface.















  A. Gauss' Law is useful when we have charge distributions that are symmetrical.





  B. It would be good to review the geometry of spheres and cylinders at this time.











Examples

1. What is the total flux through a sphere of radius R with a point charge of +Q at its center?








2. A point charge +Q is a distance of d/2 directly above the center of a square with dimensions d on a side. What is the magnitude of the flux through the square?












3. A solid copper sphere of radius a has an excess charge of +Q placed on it. This sphere is concentric and inside a second copper sphere of inner radius b and outer radius c which has an excess charge of -2Q placed on it.  Describe the electric field in all regions and the distribution of charge on each sphere.














4. A solid copper cylinder which is very long (length L) of radius a (a<<L) has an excess charge of +Q placed on it. This cylinder is concentric and inside a second copper cylinder of length L of inner radius b and outer radius c (b,c<<L) which has an excess charge of -2Q placed on it. Describe the electric field in all regions and the distribution of charge on each cylinder.