# Maxwell's Equations

Written by Jerry Ratzlaff. 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