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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 259 "" 0 "" 
{TEXT 257 125 "copyright 2000 Oregon State University              Cap
stones in Physics: Electromagnetism                  Philip J. Siemens
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 260 "" 0 "" {TEXT -1 14 "ELE
CTROMOTION\n" }}{PARA 0 "" 0 "" {TEXT -1 267 "\nThis worksheet is a le
arning tool to help visualize the fields of a linearly polarized plane
 wave reflected from a dielectric interface.  We will assume that the \+
media in which the wave propagates are insulators, so that there is no
 loss of energy due to conduction." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 53 "CHOOSE \"WINDOWS\" FROM THE \"OPTIONS/PLO
T DISPLAY\" MENU" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 81 "Our aim is to display the electric and magnetic fields as
 a function of position " }{TEXT 258 1 "r" }{TEXT -1 37 " .  We choose
 Cartesian coordinates:\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "restar
t: with (linalg): with (plots):\nrvec:=[x,y,z];\n" }}}{EXCHG {PARA 
258 "" 0 "" {TEXT -1 32 "CHARACTERIZING THE INCIDENT WAVE" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 52 "We consider reflec
tion from a boundary in the plane " }{XPPEDIT 18 0 "x=0" "6#/%\"xG\"\"
!" }{TEXT -1 11 ", i.e. the " }{XPPEDIT 18 0 "y-z" "6#,&%\"yG\"\"\"%\"
zG!\"\"" }{TEXT -1 7 " plane." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 30 "The plane of incidence is the " }{TEXT 
261 3 "x-y" }{TEXT -1 7 " plane." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 169 "The amplitude of the incident wave is ch
osen as one unit of field strength.  The wavelength of the incident wa
ve is 1 unit of distance, and its period is 1 unit of time " }{TEXT 
262 2 "t." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
39 "The direction of propagation is in the " }{TEXT 259 3 "x-y" }
{TEXT -1 23 " plane, at an angle of " }{XPPEDIT 18 0 "theta" "6#%&thet
aG" }{TEXT -1 10 " from the " }{TEXT 260 1 "x" }{TEXT -1 6 " axis." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 70 "The direc
tion of polarization of the electric field is at an angle of " }
{XPPEDIT 18 0 "alpha" "6#%&alphaG" }{TEXT -1 29 " from the plane of in
cidence." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
37 "ENTER VALUES FOR THETA AND ALPHA NOW." }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "theta:=Pi/3;alpha:=Pi/2;" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 262 "" 0 "" {TEXT -1 35 
"CHARACTERIZING THE TRANSMITTED WAVE" }}{PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{PARA 0 "" 0 "" {TEXT -1 243 "The properties of the transmitted wave
 are determined by the properties of the incident wave and the permeab
ility and susceptibility of the media.  We assume that the media are d
ielectrics but that their magnetic polarizability is negligible, " }
{XPPEDIT 18 0 "mu = mu[0]" "6#/%#muG&F$6#\"\"!" }{TEXT -1 71 " . Then \+
we only need to specify the ratio of the indices of refraction," }}
{PARA 263 "" 0 "" {TEXT -1 3 "  ." }{XPPEDIT 18 0 "n21 = n[transmitted
]/n[incident]" "6#/%$n21G*&&%\"nG6#%,transmittedG\"\"\"&F'6#%)incident
G!\"\"" }{MPLTEXT 1 0 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 43 "ENTER THE RATIO OF REFRACTIVE INDICES HERE:" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "n21:
=1.4;" }}}{EXCHG {PARA 264 "" 0 "" {TEXT -1 0 "" }}{PARA 264 "" 0 "" 
{TEXT -1 36 "CALCULATIONS OF AUXILIARY QUANTITIES" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 175 "For a detailed look at t
he incident, reflected, and transmitted waves, how they are constructe
d, how they look and how they interfere, see the worksheet \"Reflectio
n of Waves\"." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "omega:=2*Pi;\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "
thetaTran:=evalf(arcsin(sin(theta)/n21));\n" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 42 "kInc:=[2*Pi*cos(theta),2*Pi*sin(theta),0];" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 43 "kRef:=[-2*Pi*cos(theta),2*Pi*sin(theta),0
];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "kTran:=[2*Pi*cos(thetaTran)/n
21,2*Pi*sin(thetaTran)/n21,0];" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "argInc:=dotprod(rvec,kInc)-omega*t;
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "argRef:=dotprod(rvec,kRef)-omeg
a*t;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "argTran:=dotprod(rvec,kTran
)-omega*t;" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 74 "CRefPerp:=(cos(theta)-n21*cos(thetaTran))/(cos(theta)
+n21*cos(thetaTran));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "CRefPar:=(
n21*cos(theta)-cos(thetaTran))/(n21*cos(theta)+cos(thetaTran));" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "CTranPerp:=(2*cos(theta))/(cos(thet
a)+n21*cos(thetaTran));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "CTranPar
:=(2*cos(theta))/(n21*cos(theta)+cos(thetaTran));" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "eInc:=[-sin(theta)*
cos(alpha),cos(theta)*cos(alpha),sin(alpha)];" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 68 "EInc:=[cos(argInc)*eInc[1],cos(argInc)*eInc[2],cos(ar
gInc)*eInc[3]]:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "eRefPerp:=CRefPerp*
[0,0,sin(alpha)];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "eRefPar:=[-sin
(theta)*cos(alpha)*CRefPar,-cos(theta)*cos(alpha)*CRefPar,0];" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "eRef:=eRefPerp+eRefPar;" }}{PARA 0 
"> " 0 "" {MPLTEXT 1 0 69 "ERef:=[cos(argRef)*eRef[1],cos(argRef)*eRef
[2],cos(argRef)*eRef[3]]:\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "E1:
=[Heaviside(-x)*(EInc[1]+ERef[1]),Heaviside(-x)*(EInc[2]+ERef[2]),Heav
iside(-x)*(EInc[3]+ERef[3])]:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "eTranPerp:=CTranPerp*[0,0,sin(alpha
)];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "eTranPar:=[-sin(thetaTran)*c
os(alpha)*CTranPar,cos(thetaTran)*cos(alpha)*CTranPar,0];" }}{PARA 0 "
> " 0 "" {MPLTEXT 1 0 26 "eTran:=eTranPerp+eTranPar;" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 114 "ETran:=[cos(argTran)*eTran[1]*Heaviside(x),cos(
argTran)*eTran[2]*Heaviside(x),cos(argTran)*eTran[3]*Heaviside(x)]:" }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "Et
ot:=E1+ETran;" }}{PARA 0 "" 0 "" {TEXT -1 3 "\n\n\n" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 1 "\n" }}{PARA 265 "" 0 "" {TEXT -1 24 "MOTION OF E
LECTRIC FIELD" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 77 "We can collect a set of plots at different times to view \+
the time dependence." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 26 "We divide the period into " }{TEXT 263 1 "n" }{TEXT -1 
17 " equal intervals:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 5 "n:=8;" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 156 "for i from 0 to n-1 by 1 do \n\n E
[i]:=fieldplot3d(subs(t=i/n,Etot),x=-1..1,y=-1..1,z=-1..1,grid=[17,17,
3],orientation=[-135,30],axes=boxed,shading=zhue)\n\nod:" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 88 "\nNext, we
 view the plots we just made, which correspond to one cycle of the osc
illation:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 40 "for i from 0 to n-1 by 1 do \n\n E[i]\n\nod;" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 72 "\nREMEMBER THERE IS A HOMEWORK ASSIGNMENT AT THE END OF \"BOUND
ARY WAVES\"\n" }{TEXT -1 0 "" }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" 
{XPPEDIT 19 1 "" "6#%#%?G" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "" "6#%#
%?G" }{TEXT -1 0 "" }}}{EXCHG {PARA 266 "" 0 "" {TEXT -1 25 "MAGNETIC \+
FIELDS IN MOTION" }}{PARA 0 "" 0 "" {TEXT -1 75 "\nHere are the formul
as for the magnetic fields.  Be sure to check them out." }}{PARA 0 "" 
0 "" {TEXT -1 2 "  " }}{PARA 0 "" 0 "" {TEXT 264 56 "They look complet
ely different from the electric fields!" }}{PARA 0 "" 0 "" {TEXT -1 0 
"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 49 "HInc:=eval(crossprod(kInc,subs(t=0,EInc)/omega)):" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "HRe
f:=crossprod(kRef,subs(t=0,ERef)/omega):" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "H1:=[Heaviside(-x)*(HInc[1]
+HRef[1]),Heaviside(-x)*(HInc[2]+HRef[2]),Heaviside(-x)*(HInc[3]+HRef[
3])]:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 46 "HTran:=crossprod(kTran,subs(t=0,ETran)/omega):" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "Htot:=[H1[1]+HTra
n[1],H1[2]+HTran[2],H1[3]+HTran[3]];" }}{PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 156 "for i from 0 to n-1 by 1 do
 \n\n H[i]:=fieldplot3d(subs(t=i/n,Htot),x=-1..1,y=-1..1,z=-1..1,grid=
[17,17,3],orientation=[-135,30],axes=boxed,shading=zhue)\n\nod:" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "\n
 " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
40 "for i from 0 to n-1 by 1 do \n\n H[i]\n\nod;" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}{PARA 8 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 72 "Don;t
 forget to check out what happens when you change the polarization!" }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}}{EXCHG {PARA 261 "" 0 "" {TEXT -1 24 "version 22 February 2000" }}}}
{MARK "9 2 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }