Gauss’ Law

This lecture is based on HRW, Sections 24.1-24.5

Coulomb’s Law provides one way to solve problems involving
electricity — but it can sometimes require big, messy
integrals.
Gauss’ Law provides a very different way to approach
certain types of problems; it can make the solution
much simpler to find.
Electric flux through a surface is defined as the dot product
of the electric field and the “vector area” of the surface,
where the “vector area” points in the direction of the normal
to the surface
Units of electric flux are N-m^2/C
Flux going INTO a closed surface is negative;
flux coming OUT OF a closed surface is positive
Gauss’ Law states that the net electric flux through any closed
surface is equal to the electic charge enclosed by that surface,
divided by the permittivity of free space (epsilon-nought)
Charges in a conductor arrange themselves so that
- the electric field within the conductor is zero
- all electric charges are on the exterior surface of the conductor
- the electric field just outside the conductor is perpendicular to
  the surface, with magnitude
```
                (surface charge density / epsilon-nought)
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