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%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
%TCIDATA{LastRevised=Thu Feb 13 15:18:37 1997}
%TCIDATA{Language=American English}
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%TCIDATA{<LINK REL="contents" HREF="Physics.tex">}
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\begin{document}


\section{Maxwell's Equations\label{Maxwell's equations}}

Maxwell's equations relate the field quantities, the charge density, and the
current density at one single point in space, through their time and space
derivatives. They contain physical information obtained from Coulomb's,
Ampere's, and Faraday's laws, and they have been modified by Maxwell's
assumption so as to satisfy the law of continuity of charge. Below are
Maxwell's equations and related equations.

\begin{center}
$
\begin{tabular}{l|l|l}
\textbf{MKS units} & \textbf{Gaussian units} &  \\ \hline\hline
$\nabla \cdot \mathbf{D}=\rho $ & $\nabla \cdot \mathbf{D}=4\pi \rho $ &  \\ 
$\nabla \cdot \mathbf{B}=0$ & $\nabla \cdot \mathbf{B}=0$ &  \\ 
$\nabla \times \mathbf{H}=\mathbf{J}+\dfrac{\partial \mathbf{D}}{\partial t}$
& $\nabla \times \mathbf{H}=\dfrac{4\pi }{c}\mathbf{J}+\dfrac{1}{c}\dfrac{%
\partial \mathbf{D}}{\partial t}$ &  \\ 
$\nabla \times \mathbf{E}=-\dfrac{\partial \mathbf{B}}{\partial t}$ & $%
\nabla \times \mathbf{E}=-\dfrac{1}{c}\dfrac{\partial \mathbf{B}}{\partial t}
$ &  \\ 
$\mathbf{F}=q\left( \mathbf{E+v\times B}\right) $ & $\mathbf{F}=q\left( 
\mathbf{E+\dfrac{1}{c}v\times B}\right) $ & Lorentz force law \\ 
$\mathbf{D}=\epsilon _{0}\mathbf{E+P}$ & $\mathbf{D}=\mathbf{E+}4\pi \mathbf{%
P}$ & (general) \\ 
$\mathbf{D}=\epsilon _{0}\mathbf{E}$ & $\mathbf{D}=\mathbf{E}$ & (free space)
\\ 
$\mathbf{D}=\epsilon \mathbf{E}$ & $\mathbf{D}=\varkappa \mathbf{E}$ & 
(isotropic linear dielectric) \\ 
$\mathbf{B}=\mu _{0}\left( \mathbf{H}+\mathbf{M}\right) $ & $\mathbf{B}=%
\mathbf{H}+4\pi \mathbf{M}$ & (general) \\ 
$\mathbf{B}=\mu _{0}\mathbf{H}$ & $\mathbf{B}=\mathbf{H}$ & (free space) \\ 
$\mathbf{B}=\mu \mathbf{H}$ & $\mathbf{B}=\mu \mathbf{H}$ & (isotropic
linear magnetic medium)
\end{tabular}
\bigskip $
\end{center}

\vspace{1pt}The symbols used in the above equations have the following
meaning.\bigskip

\begin{center}
\begin{tabular}{|l|l|l|l|}
\textbf{Symbol} & \textbf{Meaning} & \textbf{MKS units} & \textbf{Gaussian
units} \\ \hline\hline
$\mathbf{B}$ & magnetic induction & $\unit{T}$ (tesla) & $\unit{G}$ (gauss)
\\ 
$c$ & velocity of light & $\unit{m}/\unit{s}$ (meters per second) & $\unit{cm%
}/\unit{s}$ (centimeters per second) \\ 
$\mathbf{D}$ & electric displacement & $\unit{N}/\unit{C}$ (newtons per
coulomb) & (dynes per statcoulomb) \\ 
$\mathbf{E}$ & electric field strength & $\unit{N}/\unit{C}$ (newtons per
coulomb) & (dynes per statcoulomb) \\ 
$\mathbf{F}$ & magnetic force & $\unit{N}$ (newton) & $\unit{dyn}$ (dyne) \\ 
$\mathbf{H}$ & magnetic field intensity & $\unit{A}/\unit{m}$ (amperes per
meter) & $\unit{G}$ (gauss) \\ 
$\mathbf{J}$ & current density & $\unit{A}/\unit{m}^{2}$ (amperes per square
meter) & $\unit{G}/\unit{m}$ (gauss per meter) \\ 
$\mathbf{M}$ & magnetization & $\unit{A}/\unit{m}$ (amperes per meter) & $%
\unit{G}$ (gauss) \\ 
$q$ & charge & $\unit{C}$ (coulomb) & (statcoulomb) \\ 
$\rho $ & volume charge density & $\unit{C}/\unit{m}^{3}$ (coulomb per cubic
meter) & (statcoulomb per cubic centimeter) \\ 
$\mathbf{v}$ & velocity & $\unit{m}/\unit{s}$ (meters per second) & $\unit{cm%
}/\unit{s}$ (centimeters per second)
\end{tabular}

\strut
\end{center}

\subsection{\ Related Reference Topics}

{\small \hyperref{Calculus}{}{}{../Mathematics/CAL_contents.tex}}

{\small \hyperref{Differential Equations}{}{}{../Mathematics/ODE_contents.tex%
}}

{\small \hyperref{Matrix Algebra}{}{}{../Mathematics/MA_contents.tex}}

{\small \hyperref{Table of Integrals}{}{}{%
../Mathematics/TAB_integrals.tex#table of integrals}}

{\small \hyperref{Table of Derivatives}{}{}{%
../Mathematics/TAB_derivatives.tex}}

{\small \hyperref{Table of Physical Constants}{}{}{PhysicalConstants.tex}}

{\small \hyperref{Table of SI Units}{}{}{SIUnits.tex}}

\subsection{\ Related Scientific Notebook Topics}

{\small \hyperref{Basic Techniques for Doing Mathematics}{}{}{%
../../Help/DM1.tex}}

{\small \hyperref{Numbers, Functions, and Units}{}{}{../../Help/DM2.tex}}

{\small \hyperref{Algebra}{}{}{../../Help/DM3.tex}}

{\small \hyperref{Trigonometry}{}{}{../../Help/DM4.tex}}

{\small \hyperref{Function Definitions}{}{}{../../Help/DM5.tex}}

{\small \hyperref{Plotting Curves and Surfaces}{}{}{../../Help/DM6.tex}}

{\small \hyperref{Calculus}{}{}{../../Help/DM7.tex}}

{\small \hyperref{Matrix Algebra}{}{}{../../Help/DM8.tex}}

{\small \hyperref{Vector Calculus}{}{}{../../Help/DM9.tex}}

{\small \hyperref{Differential Equations}{}{}{../../Help/DM10.tex}}

{\small \hyperref{Vectors}{}{}{../../Help/DM9-1.tex#Vectors}}

{\small \hyperref{Gradient, Divergence, and Curl}{}{}{%
../../Help/DM9-2.tex#Gradient}}

{\small \hyperref{Plots of Vector Fields and Gradients}{}{}{%
../../Help/DM9-3.tex#Vector field}}

{\small \hyperref{Scalar and Vector Potentials}{}{}{%
../../Help/DM9-4.tex#Scalar potential}}

\rule{0.67in}{0.01in}

\quad {\small Index entries: \hyperref{Inner product}{}{}{%
../../Help/DMIndex.tex#Inner product}, \hyperref{Vector calculus}{}{}{%
../../Help/DMIndex.tex#Vector calculus}, \hyperref{Vector field}{}{}{%
../../Help/DMIndex.tex#Vector field}}\hfill

\noindent \hrulefill

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"0.9959";cropright "0.9937";cropbottom "0";filename
'Nblogo.wmf';file-properties "XNPEU";}}Reference Library}{}{}{%
../ReferenceIndex.tex}}
\end{tabular}
\end{center}

\noindent \hrulefill

\end{document}
