Numerit[WIN32][1700][1703]D6{99 qffffff)@j@fffffvq@?@ffffff9@?@ffffff9@ffffff)@ffffff)@         Times New RomanArialSymbol Courier New??? G GzQ@K7AP@E_R_yE_R_x?@@ >@>@>@>@>@ >@ >@ >@>@>@>@>@>@ >@ >@  ???>>??-1.51.50.50.010.01-1.51.50.50.010.01G ~jL@K7AP@yx0>@@ >@>@>@>@>@>@ >@ >@ >@>@>@>@>@>@ >@   ???>>??-1.51.50.50.010.01-0.50.50.50.010.01X fffffv1@ffffff@tP X%Ob@eKk!R@(@ p2&WordMicrosoft Word  "System 0-@Times New RomanLSwUSw0-  2  &- ---& ?33--;  --&&T-&-- f-B( f>|-(X ---&--(X--&{@Times New RomanLSwUSw0- 33{ "System 0--2  . 33--2 ~ .' 33 '&W u&-- f-B( f|>-p$[ ---&--p$[--&W<- 33W< --2 @ . 33--2 < .' 33 '&-f- $ $--&&"-f- $ $IG $ac $  $!#ig $|rj $dl)Z'R $ALCTB: $4<+#--&&K)-f- $'!! $ $   $yzcb $QR:9 $() $ $ $ $on $\]FE $34 $   $ $ $zy $hi}RwQ} $?y@s)m(s $oici $d^Y_ $ZTNT--&&+y-f- $,46!. $)1'90;23 $;69>A@C8 $L:JBSEU= $]?[GdJfB $oDmLuNwF $I~QSK $NVXP $RZ]U $W_bZ $\df^ $slV--&&(-- $$$ $ --&&D-- $ ))  $% $%=--&&dp-f- $}z $vl $i~--&-33- ;\-- ۘ-Պ- I-- )/@Times New RomanLSwUSw0- 332 //(Master"?"" 2 / /( $ - 332 ~/(charge [%"" 2 ~/(+& 2 ~/(]@Times New RomanLSwUSw0- 2 /(  '--TO--Dm@Times New RomanLSwUSw0-  33Dm -- 2 p+. 33-- 2 m+.' 33Dm -- 2  . 33-- 2  .' 33 '--U--ss@Times New RomanLSwUSw0-  33ss -- 2 v-. 33-- 2 s-.' 33ss -- 2  . 33-- 2  .' 33 '--9O--)m-  33)m -- 2 p-. 33-- 2 m-.' 33)m -- 2  . 33-- 2  .' 33 '&Zeۘ- Պ- g[- - rrw{- 332 w{wqrTest"-" 2 wU{wqr $ - 332 {wqrcharge%""- 2 W{wqr  '--c--sF-  33sE -- 2 [. 33-- 2 [.' 33sE -- 2 -. 33-- 2 -.' 33sE -- 2 ]. 33-- 2 ].' 33sE -- 2 # . 33-- 2   .' 33 'ۘ- Պ-  K- - k-  33(2 k~Axial forces cancel)-2 Ok~ ( 2 m k~red & pink) &  - 2 Tk~ ( 'ۘ- Պ- ])v- - y=:- 332 ; :<yRe!2 ;B :<ymaining is a %     2 ;::<yse22 ;M:<yinusoidal transverse force    2 ;G:<y (blue)  - 2 3:<y e '&3k-- $==44v4v=$m=m4h5d5e>h> $\@[7R8SA $KCI;@=BE $:H7@.C1K$ )N&F&F#HJ!Q)N&K&O$UNR RYX $ ^W\c $hagn $smsy$yz$ $ $ $$ $ $ $ $  $$''$ $0099 $BCKJ $SU^\$dfjolj $ux} $ $$$ $ $ $$$  $#' $/,47 $?= F H$PNQXYQ$b ahjj h  $s s||  $   $  $ $   $ $$$$  $! $"(.( $-492$7>@C<:$AHKLEE $IPTM $PzX}[tSq $Vi^k`cXa$ZXbZdTdQ[P[T $]GfHg?^> $_5h5h,_, $_#h#h_$_hg g^ ^  $\ed[ $Zb`X $U]ZR$ OWWUTLORN$HPKKDE $@GB; $6=81 $,3-&$ '}$z v|$vpkj qq $k d_f $aZU\ $WPLS$ OHHFDLOKN$IA>>FG $D<:B $@76? $>54=-- &&%~--  $**33 $<<EE $Ix G-- &-vvvpvvvpvvvpvvvpvvvpvvvpvvv1vvv0Rotating Charge Generating Sinusoidal ForceGvvv.Uri Levy August 31, 1999vvvEvvv.Shown is the classical projection of a rotating charge on the vertical axis to generate a sinusoidal up-and-down motion. This motion is then used to explain the transverse sinusoidal force exerted by a "master charge" (a single electron rotating around a nucleus) on a distant "test charge", as shown in the figure below. Mvvv.All of that is leading to "waves" (see another posted Numerit simulation).vvv+vvv.Elapsed time =0" .secondsvvv  ! =vvv;BB !"Master" charge !"Test" chargevvv vvv >vvv.Rotating Charge Generating a Sinusoidal Transverse Forcevvv vvv $  q8ffffff)@j@fffffvq@?@ffffff9@?@ffffff9@ffffff)@ffffff)@         Times New RomanArialSymbol Courier New )` A rotating charge -` Projection on a vertical axis` Uri Levy - 31/8/99` initializations` work arrays E_R[2]:0+0j E_R_x[2]:0 E_R_y[2]:0 ` parametersf = 8 ` frequencyT = 1/f ` periodw = 2*pi*f ` angular frequencydt = T/100 ` time interval` loop over timefor t = 0 to 10 by dt"` Here we define E_R_x and E_R_y ` that are displayed by the left` Graph Viewer in the document.` We assign values only to the` second element of each array` and leave the first element` unmodified (i.e., 0)E_R[2] = 1.3*exp(1j*w*t)E_R_x[2] = real(E_R[2])E_R_y[2] = imag(E_R[2])` Here we define the values` that are displayed in the` right Graph Viewer y = E_R_y[2]x0 = 0` refresh the viewers and pause` for a while (the parameter in` the "wait" command determines` the speed of the animation)refresh wait .01d:\program files\numerit\  E_RE_R_x E_R_y fTwdtt y x0  Y 4  @, 4 , 4 ,   C B B  C   X8 4   B BB 4 4 4 4 4!  '( N6(UX 2@00j8 @1?100Y@10$@1.3?1j?.01{Gz?