modified: advancedantennaProblemSet3Problem1.tex

deleted: dualFarField.tex modified: ../ece1229/chapter4Notes.tex new file: ../ece1229/chapter4NotesPart2.tex new file: ../ece1229/dualFarField.tex
peeterjoot · Feb 28, 2015 · a0ece31 · a0ece31
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diff --git a/bin/latexRegex.pl b/bin/latexRegex.pl
@@ -86,6 +86,8 @@
 #s/\\up\b/\\uparrow/g ;
 #s/\\Veff/V_{\\mathrm{eff}}/g ;
 #s/\\Veph/V_{\\mathrm{e,ph}}/g ;
+#s/\^a/^{(a)}/g;
+#s/\^b/^{(b)}/g;
 #s/\^classical/^{\\mathrm{classical}}/g ;
 #s/\bialpha\b/{i_\\alpha}/g ;
 #s/\tY\b/\\tilde{Y}/g ;
@@ -136,5 +138,5 @@
 #s/pidotalpha/\\dot{p}_{i_\\alpha}/g ;
 #s/xialpha\b/x_{i_\\alpha}/g ;
 #s/xidotalpha/\\dot{x}_{i_\\alpha}/g ;
-s/\^a/^{(a)}/g;
-s/\^b/^{(b)}/g;
+s/_eo/_{\\textrm{eo}}/g ;
+s/_mo/_{\\textrm{mo}}/g ;
diff --git a/env/.aspell.en.prepl b/env/.aspell.en.prepl
@@ -127,8 +127,8 @@ sttress stress
 divding dividing
 coloumb's Coulomb's
 gausses Gauss's
-cooresponds corresponds
 waave wave
+cooresponds corresponds
 diagonize diagonalize
 convience convenience
 refections reflections

diff --git a/env/.aspell.en.pws b/env/.aspell.en.pws
@@ -12,8 +12,8 @@ interferometer
 relativistic
 integrands
 extremum
-Ficks
 Fick's
+Ficks
 pseudoinverse
 unstretched
 orthonormalization
@@ -207,8 +207,8 @@ Hestenes's
 imaginaries
 n'l'm
 nlm
-PDE
 Lut
+PDE
 quantized
 Guoy
 Minkowski
@@ -399,37 +399,37 @@ Routhian
 dk
 dL
 dm
-dn
 dN
-dp
+dn
 dP
+dp
 Debye
-dQ
 dq
+dQ
 Doran
-dR
 dr
+dR
 ds
 dt
 du
 intrinsics
-dV
 dv
+dV
 dw
-dx
 dX
+dx
 dy
 Prandtl
 ia
 isync
 inferometer
-iB
 ib
+iB
 eV
 ic
 dimensionalize
-iE
 ie
+iE
 ParametericPlot
 worldlines
 NaCl
@@ -455,8 +455,8 @@ mE
 delocalized
 iz
 Lasenby
-l'm
 lm
+l'm
 pathlengths
 Strang's
 xyz
@@ -467,8 +467,8 @@ mn
 kx
 Eulerian
 jellium
-nl
 n'l
+nl
 nm
 Etalon
 nn

diff --git a/notes/blogit/advancedantennaProblemSet3Problem1.tex b/notes/blogit/advancedantennaProblemSet3Problem1.tex
@@ -3,7 +3,6 @@
 % Licenced as described in the file LICENSE under the root directory of this GIT repository.
 %
 \makeproblem{Superposition of electric and magnetic dipoles}{advancedantenna:problemSet3:1}{ 
-
 An infinitesimal electric dipole of electric current strength \( I_{\textrm{eo}} \) is oriented along the x-axis. With this there is also an infinitesimal magnetic dipole of magnetic current strength \( I_{\textrm{mo}} \) but oriented along the y-axis.
 
 \makesubproblem{}{advancedantenna:problemSet3:1a}
@@ -20,11 +19,133 @@
 \makeanswer{advancedantenna:problemSet3:1}{ 
 \makeSubAnswer{}{advancedantenna:problemSet3:1a}
 
-TODO.
+The far field electric field induced by the electric current can be calculated with the transverse projection
+
+\begin{dmath}\label{eqn:advancedantennaProblemSet3Problem1:20}
+\BE_\txte
+= - j \omega \Proj_\T \BA
+= - j \omega \lr{ \BA - (\BA \cdot \kcap) \kcap },
+\end{dmath}
+
+where
+
+\begin{dmath}\label{eqn:advancedantennaProblemSet3Problem1:40}
+\BA = \xcap \frac{\mu_0 I_{\textrm{eo}} l}{4 \pi r} e^{-j k r}.
+\end{dmath}
+
+To simplify this, note that the Cartesian to spherical coordinates mapping is
+
+\begin{subequations}
+\label{eqn:advancedantennaProblemSet3Problem1:60}
+\begin{dmath}\label{eqn:advancedantennaProblemSet3Problem1:80}
+\xcap = \sin\theta \cos\phi \kcap + \cos\theta \cos\phi \thetacap - \sin\phi \phicap
+\end{dmath}
+\begin{dmath}\label{eqn:advancedantennaProblemSet3Problem1:100}
+\ycap = \sin\theta \sin\phi \kcap + \cos\theta \sin\phi \thetacap + \cos\phi \phicap
+\end{dmath}
+\begin{dmath}\label{eqn:advancedantennaProblemSet3Problem1:120}
+\zcap = \cos\theta \kcap - \sin\theta \thetacap,
+\end{dmath}
+\end{subequations}
+
+so
+
+\begin{dmath}\label{eqn:advancedantennaProblemSet3Problem1:140}
+\BE_\txte
+= - j \omega 
+\lr{ \cos\theta \cos\phi \thetacap - \sin\phi \phicap }
+\frac{\mu_0 I_{\textrm{eo}} l}{4 \pi r} e^{-j k r}.
+\end{dmath}
+
+For the magnetic current, first note that the far field magnetic field for an electric current can also be expressed in terms of the magnetic vector potential
+
+\begin{dmath}\label{eqn:advancedantennaProblemSet3Problem1:160}
+\BH 
+= \inv{\eta} \kcap \cross \BE
+= -j\frac{\omega}{\eta} \kcap \cross \lr{ \BA - (\BA \cdot \kcap)\kcap }
+= -j\frac{\omega}{\eta} \kcap \cross \BA.
+\end{dmath}
+
+Duality provides the far field electric field given an electric vector potential
+
+\begin{dmath}\label{eqn:advancedantennaProblemSet3Problem1:180}
+\BE_\txtm = j \omega \eta \kcap \cross \BF.
+\end{dmath}
+
+For the y-axis oriented magnetic current, the vector potential is
+
+\begin{dmath}\label{eqn:advancedantennaProblemSet3Problem1:200}
+\BF = \ycap \frac{\epsilon_0 I_{\textrm{mo}} l}{4 \pi r} e^{-j k r}.
+\end{dmath}
+
+The electric field will be directed along
+
+\begin{dmath}\label{eqn:advancedantennaProblemSet3Problem1:220}
+\kcap \cross \ycap
+=
+\kcap \cross 
+\lr{
+\sin\theta \sin\phi \kcap + \cos\theta \sin\phi \thetacap + \cos\phi \phicap
+}
+=
+\cos\theta \sin\phi \phicap - \cos\phi \thetacap,
+\end{dmath}
+
+so
+
+\begin{dmath}\label{eqn:advancedantennaProblemSet3Problem1:240}
+\BE_\txtm 
+= j \omega \eta 
+\lr{
+\cos\theta \sin\phi \phicap - \cos\phi \thetacap
+}
+\frac{\epsilon_0 I_{\textrm{mo}} l}{4 \pi r} e^{-j k r}.
+\end{dmath}
+
+Summing \cref{eqn:advancedantennaProblemSet3Problem1:140}, and \cref{eqn:advancedantennaProblemSet3Problem1:240} gives
+
+%\begin{dmath}\label{eqn:advancedantennaProblemSet3Problem1:260}
+\boxedEquation{eqn:advancedantennaProblemSet3Problem1:260}{
+\BE 
+= 
+j \omega 
+\frac{l}{4 \pi r} e^{-j k r} \eta \epsilon_0
+\lr{
+\lr{ -\cos\theta \cos\phi \thetacap + \sin\phi \phicap } \eta I_{\textrm{eo}} 
++
+\lr{  \cos\theta \sin\phi \phicap - \cos\phi \thetacap } I_{\textrm{mo}} 
+}
+}
+%\end{dmath}
+
 \makeSubAnswer{}{advancedantenna:problemSet3:1b}
 
-TODO.
+When \( \eta I_{\textrm{eo}} = I_{\textrm{mo}} \), this reduces to
+
+\begin{dmath}\label{eqn:advancedantennaProblemSet3Problem1:280}
+\BE 
+= 
+j \omega 
+\frac{\mu_0 I_{\textrm{eo}} l}{4 \pi r} e^{-j k r}
+\lr{ 1 + \cos\theta } 
+\lr{
+-\cos\phi \thetacap 
++ \sin\phi \phicap 
+}.
+\end{dmath}
+
 \makeSubAnswer{}{advancedantenna:problemSet3:1c}
 
-TODO.
+In the zy plane, \( \phi = \pi/2 \), and the electric field has only a \( \phicap \) component
+
+\begin{dmath}\label{eqn:advancedantennaProblemSet3Problem1:n}
+\BE 
+= 
+j \omega 
+\frac{\mu_0 I_{\textrm{eo}} l}{4 \pi r} e^{-j k r}
+\lr{ 1 + \cos\theta } 
+\phicap 
+\end{dmath}
+
+PLOT: TODO.
 }
diff --git a/notes/blogit/dualFarField.tex b/notes/blogit/dualFarField.tex
diff --git a/notes/blogit/renumber b/notes/blogit/renumber
@@ -10,7 +10,7 @@
 #~/bin/lgrep numberGame.tex | tee o ; . ./o
 #~/bin/lgrep pathria72typoPossibility.tex | tee o ; . ./o
 #~/bin/lgrep pipeFlowConstPressureGradient.tex  | tee o ; . ./o
-~/bin/lgrep t.tex | tee o ; . ./o
+#~/bin/lgrep t.tex | tee o ; . ./o
 #perl -p -i ./p ../blogit/bitcoin.tex
 #perl -p -i ./p ../blogit/mortgageInterest.tex
 #perl -p -i ./p ../blogit/numberGame.tex
@@ -28,23 +28,16 @@
 #~/bin/lgrep advancedantennaProblemSet3.tex | tee o ; . ./o
 #perl -p -i ./p ../blogit/advancedantennaProblemSet3.tex
 
-#~/bin/lgrep advancedantennaProblemSet3Problem1.tex | tee o ; . ./o
+~/bin/lgrep advancedantennaProblemSet3Problem1.tex | tee o ; . ./o
 #~/bin/lgrep advancedantennaProblemSet3Problem2.tex | tee o ; . ./o
 #~/bin/lgrep advancedantennaProblemSet3Problem3.tex | tee o ; . ./o
 #~/bin/lgrep advancedantennaProblemSet3Problem4.tex | tee o ; . ./o
 #~/bin/lgrep advancedantennaProblemSet3Problem5.tex | tee o ; . ./o
-#perl -p -i ./p ../blogit/advancedantennaProblemSet3Problem1.tex
+perl -p -i ./p ../blogit/advancedantennaProblemSet3Problem1.tex
 #perl -p -i ./p ../blogit/advancedantennaProblemSet3Problem2.tex
 #perl -p -i ./p ../blogit/advancedantennaProblemSet3Problem3.tex
 #perl -p -i ./p ../blogit/advancedantennaProblemSet3Problem4.tex
 #perl -p -i ./p ../blogit/advancedantennaProblemSet3Problem5.tex
 
 #~/bin/lgrep chapter5Notes.tex | tee o ; . ./o
 #perl -p -i ./p ../blogit/chapter5Notes.tex
-
-#~/bin/lgrep reciprocityTheorem.tex | tee o ; . ./o
-#perl -p -i ./p ../blogit/reciprocityTheorem.tex
-
-
-~/bin/lgrep dualFarField.tex | tee o ; . ./o
-#perl -p -i ./p ../blogit/dualFarField.tex
diff --git a/notes/blogit/tex2mathjax b/notes/blogit/tex2mathjax
@@ -117,7 +117,9 @@ foreach (@$rLines)
    s/\\textAndIndex{(.*?)}/$1/g ;
    s/\\implies/\\Rightarrow/g ;
    s/\\chaptext/ch./g ;
+   s/\\tabtext/tab./g ;
    s/\\S/section/g ;
+   s/\\Proj\b/\\textrm{Proj}/g ;
 
    s/^ *%.*// ;
    s/^ *\\input.*// ;

diff --git a/notes/ece1229/METADATA b/notes/ece1229/METADATA
@@ -106,6 +106,14 @@ my @ece1229 =
    URL => 'http://peeterjoot.com/archives/math2015/gaMagneticSourcesToTensorToVector.pdf',
    WHAT => qq()
 }
+,{
+   SOURCE => 'dualFarField',
+   TITLE => qq(Duality transformation of the far field fields.),
+   DATE => 'February 27, 2015',
+   REF => 'dualFarField',
+   URL => 'http://peeterjoot.com/archives/math2015/dualFarField.pdf',
+   WHAT => qq()
+}
 ) ; # @ece1229
 return @ece1229 ;
 }