AP Physics C: Electricity and Magnetism / Unit 8: Electric Charges, Fields, and Gauss's Law
8.4 Electric Fields of Charge Distributions
Notes
For continuous charge, integrate: $\displaystyle \vec E=\int\frac{k\,dq}{r^2}\hat r$.
- Infinite line: $\displaystyle E=\frac{\lambda}{2\pi\varepsilon_0r}$.
- Infinite plane: $\displaystyle E=\frac{\sigma}{2\varepsilon_0}$ (uniform).
- On the axis of a ring, symmetry cancels the perpendicular parts.
Practice
The field of an infinite charged plane:
Uniform.
The field of a long line charge falls off as:
Cylindrical symmetry.
At the center of a uniformly charged ring, the field is:
Contributions cancel.
Ready for more? Take the Unit 8 test.