PX284 - O2 - electric and magnetic fields

electric ( $\vec{E} (\vec{r}, t)$ ) and magnetic ( $\vec{B} (\vec{r}, t)$ ) are vector fields that affect charged particles, given by the lorentz force:

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

maxwell's equations (integral form)

gauss' law

PX157 - B5a - gauss's law
the electric field through a closed surface is given by:

\subset \supset \iint_{S} \vec{E} \cdot d \vec{S} = \frac{Q_{encl.}}{ε_{0}} = ∭_{V} \frac{ρ}{ε_{0}} d V

where,
$Q_{encl.}$ is the charge enclosed by the surface $S$ ,
$ε_{0}$ is the permittivity of free space,
$ρ$ is the charge density,
$V$ is the volume enclosed by the surface $S$ .

solenoidal condition

AKA the 'law with no name'
the magnetic field through a closed surface is given by:

\subset \supset \iint_{S} \vec{B} \cdot d \vec{S} = 0

this says that there are no magnetic monopoles, ie. magnetic charges

faraday-lenz law

the emf around a circuit is given by:

ϵ = \oint_{C} \vec{E} \cdot d \vec{l} = - \frac{d}{d t} \iint_{S} \vec{B} \cdot d \vec{S}

ie. it is the rate of change of magnetic flux

ampere's law

the magnetic field around a closed loop is given by:

\oint_{C} \vec{B} \cdot d \vec{l} = μ_{0} I_{encl.} = μ_{0} \iint_{S} \vec{J} \cdot d \vec{S}

where, $I_{encl.}$ is the current enclosed by the loop, $μ_{0}$ is the permeability of free space, and $\vec{J}$ is the current density