


H 

Gauss's
Law 





H 

Calculating
the Electric Field 

Dr. Walter Lewin, MIT

The Electric Universe,
by David Bodanis 

Using
Coulomb's Law we were able to calculate the
Electric Field for a few charge distributions.
We will develop a different method to calculate the Electric
Field. Using symmetry and the fundamental inverse square law we
will derive Gauss's Law.








Electric
Flux is proportional to the number of electric field lines penetrating
some surface 



















Mechanical
Universe
Karl Friedrich Gauss



In
principle, Gauss's Law can be solved for E to determine
the electric field due to a system of charges or a continuous distribution
of charge. In practice, however, this type of solution is applicable
only in a limited number of highly symmetric situations.
I told you this would be easy and fun. . .
Determining
the Gaussian Surface to use in our cacluations:
1. The value of the electric field can be argued by symmetry to be constant
over the surface
2. The dot product in Gauss’s Law can be expressed as a simple
algebraic product E dA
because E and dA are parallel.
3. The dot product in Gauss’s Law is zero because E and dA are perpendicular.
4. The field can be argued to be zero over the surface.







a video
of all this. . .and a how about the EField of a Cylinder? 






Mechanical
Universe
Michael Faraday


















Wait until the movie has loaded (68 MB). Click your way through the solution.


















