PHYS 208 Lecture 7

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Exam Tonight at 7:30 over everything up to Ch. 23.2

Important Formulas

Constants

$\begin{array}{rl}k& =\frac{1}{4\pi {ϵ}_0}=8.99\times 10^9\\ {ϵ}_0& =8.85\times 10^{-12}\end{array}$

Coulomb's Law

$\begin{array}{rl}F& =k\frac{q_1{q}_2}{r^2}\\ \overrightarrow{F}& =k\frac{q_1{q}_2}{r^2}\hat{r}\end{array}$

Electric Field

$\begin{array}{rl}E& =k\frac{q}{r^2}\\ \overrightarrow{E}& =k\frac{q}{r^2}\hat{r}\end{array}$

Corollaries

$\begin{array}{rl}F& =qE\\ \overrightarrow{F}& =q\overrightarrow{E}\end{array}$

Gauss' Law (Electric Flux)

$\begin{array}{rlr}\mathrm{\Phi }& =\oint \overrightarrow{E}\cdot \mathrm{d}\overrightarrow{A}=EA& =\frac{q_{\mathrm{i}\mathrm{n}}}{{ϵ}_0}\end{array}$

Reverse-engineering for Electric fields can only be computed for the following cases:

1. spherically symmetric distributions (radially outward (+) or inward (−))
2. uniformly charged infinite planes (normal/perpendicular to the plane pointing away (+) or toward (−) on both sides)
3. uniformly charged infinitel lines (cylindrically radially outward (+) or inward (−) along line's axis)