H Gauss's Law  
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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 E-Field of a Cylinder?
Mechanical Universe
Michael Faraday

Quick Quiz 24
Wait until the movie has loaded (68 MB). Click your way through the solution.