EMEC - Greg

Definitions

Symbol	Units	Name
$\overrightarrow{E}$	$\frac{V}{M}$	Electric Field Intensity
$\overrightarrow{D}$	$\frac{C}{M^2}$	Electric Flux Density
$\overrightarrow{H}$	$\frac{A}{M}$	Magnetic Field Intensity
$\overrightarrow{B}$	$T=\frac{W}{M^2}$	Magnetic Flux Density

Analogies between Electric & Magnetic Circuits

Electric	Magnetic
$V=\int \overrightarrow{E}\cdot \overrightarrow{dl}$	$\overrightarrow{F}=\int \overrightarrow{H}\cdot \overrightarrow{dl}$
$\sum _n{V}_n=0=\oint \overrightarrow{E}\cdot \overrightarrow{dl}$ Kirchoff's voltage law	$\oint \overrightarrow{H}\cdot \overrightarrow{dl}=N\cdot i=\sum _{n}H\cdot l+N\cdot i=0$
$\sum _n{I}_n=0={\oint }_S\overrightarrow{J}\cdot \overrightarrow{dS}$ Kirchoff's current law	$\oint \overrightarrow{B}\cdot \overrightarrow{dS}=0$ The B-field has to go around in a loop
$\oint \overrightarrow{J}\cdot \overrightarrow{dS}=I$	$\int \overrightarrow{B}\cdot \overrightarrow{dS}=\stackrel{phi}{\overbrace{\mathrm{\Phi }}}$ Magnetic flux
$R=\frac{V}{I}$	$\stackrel{reluctance}{\overbrace{R}}=\frac{F}{\mathrm{\Phi }}=\frac{N\cdot i}{\mathrm{\Phi }}$
$I=\frac{V}{R}=G\cdot V$ or $\overrightarrow{J}=\sigma \cdot \overrightarrow{E}$	$\overrightarrow{B}=\mu \cdot H$ assumed linearity (though it's not always the case - think hysteresis loop

Parenthesizing big expressions, brackets, bars

Feature	Syntax	How it looks rendered
Bad	( \frac{1}{2} )	$(\frac{1}{2})$
Good	\left ( \frac{1}{2} \right )	$\left(\frac{1}{2}\right)$