Maxwell's Equations

Written by Jerry Ratzlaff on . Posted in Electromagnetics

Maxwell's Equations describe electromagnetics, how electric and magnetic fields interact, propagate and are influenced by objects.

formula

Equation 1: Gauss' Law  

  • \( \bigtriangledown \cdot D = \rho_v \)

Equation 2: Gauss' Law for Magnetism

  • \( \bigtriangledown \cdot B = 0\)

Equation 3: Faraday's Law of Induction 

  • \( \bigtriangledown \;x\; E = \frac { \partial B} { \partial t} \)

Equation 4: Ampere's Law    

  • \( \bigtriangledown \;x\; H = \frac { \partial D} { \partial t} + J \)

Where:

\(\bigtriangledown \cdot\) = divergence operator

\(D\) = electric displacement

\(\rho\) = electric charge density

\(B\) = magnetic flux density

\(E\) = electric field strength

\(H\) = magnetic field strength

\(J\) = electric current density

\(t\) = time