tas@tasman.cc.utas.edu.au (Tasman Derk Van Ommen) (03/10/91)
Before I tear out all my hair can anyone explain LaTeX's page breaking madness
in the example that follows...
As provided here, LaTeX leaves an extraordinarily long gap at the bottom of
the first page. Bothered by this, (since there looks to be ample room for
the next paragraph) I *DUPLICATED* the paragraph which was to follow, and
behold, LaTeX decided that it could fit the duplicate paragraph on the
aforementioned "empty" first page. I am not a TeXpert by any means, but I
have RTFM (too many times) and tried \nopagebreaks with no joy.
How do I fix things?
Tas van Ommen
Physics Department,
University of Tasmania.
email: tas@physvax.phys.utas.edu.au
%========================= cut here ========================================
\documentstyle[12pt,a4]{article}
%
% Did have bfrac define line here, but tex did not like it
\def\ts{\textstyle}
\def\ds{\displaystyle}
\newcommand{\grad}{\mbox{grad\,}}
\newcommand{\secm}{${\rm sec}^{-1}$}
\newcommand{\ampm}{${\rm amp}^{-1}$}
%
% the following is an experiment for `Roman' chapter(i.e.section) titles
\renewcommand{\thesection}{\Roman{section}}
\renewcommand{\thesubsection}{\thesection-\arabic{subsection}}
\renewcommand{\thesubsubsection}{\thesubsection.\arabic{subsubsection}}
%
\setcounter{section}{2} % Actually, this is Section 3
%
\begin{document}
%
for electrostatics.
\noindent
We write the $\mu_{o}$ on the top line instread of the bottom line to
emphasize a fundamental difference between magnetic dipole and electric
dipoles. The forces between magnetic dipole {\em increase} when they are
immersed in a magnetic medium, whereas the forces between electric dipoles
{\em decrease} when they are immersed in a dielectric.\\
\subsection{Magnetic Induction, B}
\noindent
The basic field vector in the magnetic field is defined as the force per
unit pole. We cannot give this the name `magnetic field strength' by
analogy with \underline{E}, the electric field strength, as this name has
been given to another field vector we will encounter later. The force per
unit pole is called the {\em magnetic induction, B}\@. \underline{B} is
sometimes called the magnetic flux density. Its unit in the MKSA system is
the weber $\mbox{m}^{-2}$ (see Section IV.1).\\
\noindent
\samepage{In practice \underline{B} cannot be measured directly as prescribed
in its definition as poles do not exist singly. However the torque
experienced by a dipole is given by \\}
%
% Diagram top right on Page: III - 5
\parbox{2.75in}
{\( \underline{\tau} \: = \: \underline{M}_{m} \, \times \, \underline{B}
(\mbox{cf.}\:\underline{\tau} \: = \: \underline{M}_{e}
\times \underline{E}\/ \: \mbox{for the electric dipole
--- Section~I.8)} \)\\
\noindent
If the axis of the dipole is at right angles to the field $\tau = MB$\/ i.e.
the magnetic induction at a point in the field is the torque experienced
per unit dipole by a dipole placed so that its axis is at right angles to
the field, the direction of \underline{B} being given by right hand screw.
Thus \underline{B} can be determined everywhere in the field by observation
of the torque experienced by a dipole of known moment.} \\
% DUPLICATE PARAGRAPH - UNCOMMENT THIS AND IT WILL APPEAR AT THE BOTTOM
% OF THE CURRENT PAGE; LEAVE THINGS AS THEY ARE AND THE IDENTICAL PARAGRAPH
% FOLLOWING MOVES TO THE NEXT PAGE!
%\noindent
%It is therefore seen that \underline{B} can be defined and discussed in
%terms of the single pole without introducing arguments which cannot be
%checked experimentally. There is no difficulty about rephrasing the
%arguments in terms of the dipole except that a greater mathematical
%complexity is thereby introduced. In the theoretical development that
%follows we will often refer to the behaviour of individual poles rather
%than dipoles in order to simplify the mathematics as much as possible.\\
\noindent
It is therefore seen that \underline{B} can be defined and discussed in
terms of the single pole without introducing arguments which cannot be
checked experimentally. There is no difficulty about rephrasing the
arguments in terms of the dipole except that a greater mathematical
complexity is thereby introduced. In the theoretical development that
follows we will often refer to the behaviour of individual poles rather
than dipoles in order to simplify the mathematics as much as possible.\\
\subsection{The Gauss Theorem in Magnetostatics (free space)}
\noindent
The field of ``point pole'' in free space,
\[ \underline{B} \: = \: \frac{\mu_{o}}{4\pi} \: \frac{p}{r^{2}} \:
\underline{\hat{r}} \]
i.e. flux of $\underline{B}$\/ through small area $\delta A$ near point pole,
\begin{eqnarray*}
\mbox{}
\delta \phi_{m} & = & \underline{B} \cdot \underline{\hat{\nu}} \delta A \\
& = & \frac{\mu_{o}}{4\pi} \; p \:\frac{\underline{\hat{r}}
\cdot \underline{\hat{\nu}} \delta A}{r^{2}} \\
& = & \frac{\mu_{o}}{4\pi} \; p \: \delta \Omega
\end{eqnarray*}
where $\delta \Omega$ is the solid angle subtended by the area at the
pole, i.e. total flux of \underline{B} through closed surface surrounding
point pole,
\[ \oint \delta \phi_{m} \: = \: \oint \underline{B} \cdot
\underline{\hat{\nu}} \delta A
\: = \: \frac{\nu_{o}p}{4 \pi} \oint d \Omega \: = \: \mu_{o}p \]
This can be extended to any number of poles, so that
\[ \oint \underline{B} \cdot \underline{\hat{\nu}} dA \; = \; \nu_{o}\Sigma p\]
However, we have seen that poles do not exist singly but only as
dipoles, so that any closed surface must contain an equal amount of north
and south pole.
Hence
\[ \oint \underline{B} \cdot \underline{\hat{\nu}} dA \; = \; 0 \]
or in differential form $\mbox{div} \underline{B} = 0$.\\
\end{document}
%====================== end of example ==================================