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

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 up previous
Next: The Wave Equation Up: Maxwell's Equations Previous: Ampère's Law
Jess H. Brewer
1999-04-07