Electromagnetism

Field

A “field” is any physical quantity which takes on different values at different points in space.

Flux

$Flux = (average\ outward\ normal\ component)\cdot(surface\ area)\tag{1}$

Circulation

$Circulation = (average\ tangential\ component)\cdot(distance\ around)\tag{2}$

The laws of electromagnetism

$\vec{F}$

Moving charge with velocity $\vec{v}$,

$\vec{F}=q(\vec{E}+\vec{v}\times \vec{B})\tag{3}$

$\vec{E}$

$The\ flux\ of\ \vec{E}\ through\ any\ closed\ surface={the\ net\ charge\ inside \over \epsilon_0}\tag{4}$

For any surface S (not closed) whose edge is the curve C,

$Circulation\ of\ \vec{E}\ around\ C=-{d \over dt}(flux\ of\ \vec{B}\ through\ S)\tag{5}$

$\vec{B}$

$Flux\ of\ \vec{B}\ through\ any\ closed\ surface=0\tag{6}$

For any surface S bounded by the curve C,

$c^2(circulation\ of\ \vec{B}\ around\ C)=-{d \over dt}(flux\ of\ \vec{E}\ through\ S)+{flux\ of\ electric\ current\ through\ S \over \epsilon_0}\tag{7}$