PHYS 208 Lecture 7

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

Important Formulas

Constants

${\begin{aligned}k&={\frac {1}{4\pi \epsilon _{0}}}=8.99\times 10^{9}\\\epsilon _{0}&=8.85\times 10^{-12}\end{aligned}}$

Coulomb's Law

${\begin{aligned}F&=k{\frac {q_{1}q_{2}}{r^{2}}}\\{\vec {F}}&=k{\frac {q_{1}q_{2}}{r^{2}}}\,{\hat {r}}\end{aligned}}$

Electric Field

${\begin{aligned}E&=k{\frac {q}{r^{2}}}\\{\vec {E}}&=k{\frac {q}{r^{2}}}\,{\hat {r}}\end{aligned}}$

Corollaries

${\begin{aligned}F&=qE\\{\vec {F}}&=q{\vec {E}}\end{aligned}}$

Gauss' Law (Electric Flux)

${\begin{aligned}\Phi &=\oint {\vec {E}}\cdot \mathrm {d} {\vec {A}}=EA&={\frac {q_{\mathrm {in} }}{\epsilon _{0}}}\end{aligned}}$

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)