PHYS 208 Lecture 3

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Note similarities in Law of Universal gravity and Coulomb's Law for electric force:

$F_{c}=k{\frac {q_{1}q_{2}}{r^{2}}}\quad \quad F_{g}=G{\frac {m_{1}m_{2}}{r^{2}}}$

Electric Fields

We've used fields before in mapping Gravitational Fields: $g={\frac {F_{g}}{m}}$

Measured in Newtons per Coulomb [N/C].

${\vec {E}}_{\mathrm {pt\ charge} }=k{\frac {q}{r^{2}}}{\hat {r}}$

${\vec {F}}=q{\vec {E}}$

• electric field of a positive charge points away from it
• electric field of a negative charge points toward it

In a system of charges, the net electric field is the vector sum of the individual fields for each charge:

${\vec {E}}=\sum _{i=1}^{n}k{\frac {q_{i}}{{r_{i}}^{2}}}{\hat {r}}_{i}={\vec {E}}_{1}+{\vec {E}}_{2}+\dots +{\vec {E}}_{n}$

Continuous Point distributions

${\vec {E}}=\int k{\frac {\mathrm {d} q}{r^{2}}}{\hat {r}}$

Common Integration Point Charges

• Linear charge distribution: $\mathrm {d} q=\lambda \mathrm {d} l$
• Surface charge distribution: 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 \mathrm{d}q = \sigma \mathrm{d}A}
• Volume charge distribution: 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 \mathrm{d}q = \rho \mathrm{d}V}