Maxwell’s Equations in MKS units

(in absence of magnetic or polarizable media)

Differential Form:

Ampere’s Law

Poisson Equation

[Absence of magnetic monopoles]

Constitutive

relations

Integral Form:

definition of magnetic flux

Ampere’s Law

definition of electric flux

Gauss’ Law for E (from Poisson’s Equation)

Gauss’ Law for B (no magnetic monopoles exist)

Also:

Lorentz force on charge q

Integrate charge density over a volume to get charge enclosed

Integrate current density over an area to get current enclosed

Integrate this over a volume to get energy contained

Poynting vector (points in the direction of and equal to energy flux)

Poynting’s Theorem

Light speed in vacuum ~ 3*108 [m/s]

Where:

Most lower case symbols are scalars ( is a vector).

Most upper case symbols are vectors ( and  are scalars).

is the curl operator

is the dell dot product operator

=  electric field intensity [V/m]

= electric flux density [C/m2]

= magnetic flux density [T]

= magnetic field strength [A/m]

= time [s]

= current density [A/m2]

= charge density [C/m3]

= permittivity [F/m]

= 8.8542*10-12 = permittivity of free space [F/m]

= permeability [H/m]

= 4*p*10-7 = permeability of free space [H/m]

integral over a closed loop or area

integral

vector dot product

vector cross product

= differential length along a path [m]

= differential area over a surface [m2]

= differential volume [m3]

= magnetic flux [Wb]

= electric flux [Cm/F]

= magnetic flux integrated over a closed surface [Wb]

= electric flux integrated over a closed surface [Cm/F]

= force [N]

= velocity [m/s]

= electric charge [C]

= electric current [A]

= energy [J]

= Poynting vector [W/m2]

Sources:    NRL Plasma Formulary and http://www.uwm.edu/~norbury/em/node36.html