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]




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)



                 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]



          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


*      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