User talk:Williamborg/sandbox4

Jørgen Brekke, born 26 April 1968 in Horten municipality, Vestfold county, Norway is a Norwegian author and journalist. He was raised in Horten, and later moved to Trondheim.

Breeke was educated as a teacher at the Norwegian University of Science and Technology in Trondheim and has worked as a journalist and personal assistant. He lives there with his wife and three children.

In 2011 he debuted with a criminal fiction novel, Nådens omkrets (published in the United States as "Where Monsters Dwell"), which has been translated into and sold in eight languages in thirty countries. It achieved substantial recognition in Norway, receiving two debut novel awards (the Norlis debutantpris and the Maurits Hansen-prisen - Nytt Blod). Vinneren av Norli debutantpris (article in Norwegian)

___Force - Coulomb's Law

 * $$F = \frac{1}{4 \pi \varepsilon_0} \frac{q_1q_2}{r^2}$$


 * $$ \begin{align} \frac{1}{4 \pi \varepsilon_0} = 8.987 \times 10^9 \ \mathrm{N \cdot m^2 / C^{2}}

\end{align} $$


 * ε0 ≈ $8.854 F·m^{−1}$

____Coulomb's law: Vector

 * $$\mathbf{F} = {1 \over 4\pi\varepsilon_0}{q_1q_2(\mathbf{r}_1 - \mathbf{r}_2) \over |

\mathbf{r}_1 - \mathbf{r}_2|^3} = {1 \over 4\pi\varepsilon_0}{q_1q_2 \over r^2}\mathbf{\hat{r}}_{21},$$

____Coulomb's law: System of discrete charges

 * $$\mathbf{F}(\mathbf{r}) = {q \over 4\pi\varepsilon_0}\sum_{i=1}^N {q_i(\mathbf{r} - \mathbf{r}_i) \over |\mathbf{r} - \mathbf{r}_i|^3} = {q \over 4\pi\varepsilon_0}\sum_{i=1}^N {q_i \over R_i^2}\mathbf{\hat{R}}_i,$$

____Definition: Electric Field


\mathbf{E} = \frac{\mathbf{F}}{q} $$

____Electric field: point charge

 * $$\mathbf{E} = {1 \over 4\pi\varepsilon_0}\frac{q}{r^2}.$$

____Electric field: multiple point charges

 * $$\mathbf{E} = \sum_{i=1}^N {1 \over 4\pi\varepsilon_0}\frac{q}{r^2}.$$

Electric Displacement Field
The permittivity ε of a linear material, which usually differ from the permittivity of free space ε0, is used to calculate the electric displacement field:


 * $$\mathbf{D} = \varepsilon \mathbf{E}. $$

____Relative permittivity
Materials generally have a higher permitivity ($$\varepsilon$$) than the permitivity in a vacuum ($$\varepsilon_{0}$$). Hence it is useful to define the relative permitivity ($$\varepsilon_{r}$$) as


 * $$\varepsilon_{r} = \frac{\varepsilon}{\varepsilon_{0}},$$

Example values are listed below