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:
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