PHYS 208 Lecture 7

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

Important Formulas

Constants

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{align} k &= \frac{1}{4\pi\epsilon_0} = 8.99 \times 10^9 \\ \epsilon_0 &= 8.85 \times 10^{-12} \end{align}}

Coulomb's Law

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{align} F &= k \frac{q_1 q_2}{r^2} \\ \vec{F} &= k \frac{q_1 q_2}{r^2} \, \hat{r} \end{align}}

Electric Field

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{align} E &= k \frac{q}{r^2} \\ \vec{E} &= k \frac{q}{r^2} \, \hat{r} \end{align}}

Corollaries

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{align} F &= qE \\ \vec{F} &= q\vec{E} \end{align}}

Gauss' Law (Electric Flux)

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{align} \Phi &= \oint \vec{E} \cdot \mathrm{d}\vec{A} = EA &= \frac{q_\mathrm{in}}{\epsilon_0} \end{align}}

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

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