Maxwell’s Equations in MKS units (in absence of magnetic or polarizable media):
Differential Form:
Faraday’s Law
Ampere’s
Law
Poisson
Equation
[Absence
of magnetic monopoles]
Constitutive
relations
Integral Form:
Faraday’s Law
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:
All lower case symbols are scalars.
Most upper case symbols are vectors (I and W are exceptions).
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
stregth [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
= 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]
F = force [N]
= velocity
[m/s]
q = electric charge [C]
I = electric current [A]
W = energy [J]
N = Poynting vector [W/m2]
Sources: NRL Plasma Formulary and http://www.uwm.edu/~norbury/em/node36.html