Maxwell's Equations

In 1865, James Clerk Maxwell assembled all the known ``Laws'' of in their most compact, elegant (differential) form, shown here in SI units:

GAUSS' LAW FOR ELECTROSTATICS:

$\begin{displaymath}\Div{D} \; = \; \rho \end{displaymath}$

(22.9)

GAUSS' LAW FOR MAGNETOSTATICS:

$\begin{displaymath}\Div{B} \; = \; 0 \end{displaymath}$

(22.10)

FARADAY'S LAW:

$\begin{displaymath}\Curl{E} + {\partial \Vec{B} \over \partial t} \; = \; 0 \end{displaymath}$

(22.11)

AMPÈRE'S LAW:

$\begin{displaymath}\Curl{H} - {\partial \Vec{D} \over \partial t} \; = \; \Vec{J} \end{displaymath}$

(22.12)

These four basic equations are known collectively as MAXWELL'S EQUATIONS; they are considered by most Physicists to be a beautifully concise summary of phenomenology.

Well, actually, a complete description of also requires two additional laws:

EQUATION OF CONTINUITY:

$\begin{displaymath}{\partial \rho \over \partial t} \; = \; - \Div{J} \end{displaymath}$

(22.13)

LORENTZ FORCE:

$\begin{displaymath}\Vec{F} \; = \; q \, \left( \Vec{E} \; + \; \Vec{v} \times \Vec{B} \right) . \end{displaymath}$

(22.14)

Next: The Wave Equation Up: Maxwell's Equations Previous: Ampère's Law

Jess H. Brewer
1999-04-07