PHYS 208 Lecture 3

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

$F_c=k\frac{q_1{q}_2}{r^2}{F}_g=G\frac{m_1{m}_2}{r^2}$

Electric Fields

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

Measured in Newtons per Coulomb [N/C].

${\overrightarrow{E}}_{\mathrm{p}\mathrm{t}\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{e}}=k\frac{q}{r^2}\hat{r}$

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

• 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:

$\overrightarrow{E}=\sum _{i=1}^{n}k\frac{q_i}{{r_i}^2}{\hat{r}}_i={\overrightarrow{E}}_1+{\overrightarrow{E}}_2+\dots +{\overrightarrow{E}}_n$

Continuous Point distributions

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

Common Integration Point Charges

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