AP Physics C: Electricity and Magnetism / Unit 8: Electric Charges, Fields, and Gauss's Law
8.6 Gauss's Law
Notes
$$\oint\vec E\cdot d\vec A=\frac{Q_{enc}}{\varepsilon_0}$$
- Choose a Gaussian surface with symmetry (sphere, cylinder, pillbox) so $E$ is constant on it.
- Outside a uniform sphere, the field is like a point charge.
Practice
The flux through a sphere enclosing $Q$ is:
Independent of radius.
Inside a uniformly charged solid sphere (radius $R$), $E$ grows as:
$Q_{enc}\propto r^3$.
Inside a charged conducting shell, $E=$
No enclosed charge.
Ready for more? Take the Unit 8 test.