Dr. Walter Lewin, MIT.mov (110 MB)
any closed surface
is equal to the charge inside the surface.
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.
When a charge distribution possesses spatial symmetry, we can find a Gaussian surface over which the electric field has a constant magnitude. If E is parallel to dA everywhere on this Gaussian surface, then the surface integral in Gauss's Law becomes
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.
Michael Faraday
