GraphingCalculator 3.5;
Window 44 6 807 1201;
PaneDivider 0;
FontSizes 18 14 12;
BackgroundType 0;
SliderControlValue 20;
2D.Scale 0.5 0.5 2 2;
2D.BottomLeft -11.3125 -17.78125;
2D.Axes 0;
2D.GraphPaper 0;
Text "Radiation from an accelerated charge.

Version 0.2 12-3-06
To do:
(i) Sort out question of transverse wave front.
(ii) Generalize to oscillating source.
(iii) Better way to generate multiple field lines?
(iv) Version in polar coordinates

c – speed of light; m – slope of field line;";
Color 2;
MathPaneSlider 53;
Expr c=slider([1,10]);
Color 4;
Expr function(m,A)=tan(A);
Expr function(Y,x,m,b)=m*x+b;
Text "Position of accelerated charge – b; bM is endpoint and D the time interval.  Maximum charge velocity is bM/D, so c should be bigger than this.";
Color 6;
Expr b_M=1,D=1;
Color 8;
Expr function(b,s)=branch(if(0,s<-0.01),if(b_M*[1-(1/D^2*[s-D]^2)],-0.01<s<D),if(b_M,s=D),if(b_M,s>D));
Color 2;
Expr vector(0,function(b,n));
Color 8;
Expr vector(0,0);
Text "Position of propagating wave fronts";
Color 5;
Expr function(X_O,s,A)=c*cos(A)*s;
Color 7;
Expr function(X_o,s,A)=-(c*cos(A)*s);
Color 6;
Expr function(Y_O,s,A)=c*sin(A)*s;
Text "Field before charge begins to accelerate:";
Color 5;
Expr function(Y_0,x,A)=[if(function(Y,x,function(m,A),0),abs(x)>max([function(X_O,n,A),function(X_o,n,A)]))];
Color 6;
Expr function(Y_0,x,T),in(T,set([-5]*pi/12,[-4]*pi/12,[-3]*pi/12,[-2]*pi/12,[-1]*pi/12,1*pi/12,2*pi/12,3*pi/12,4*pi/12,5*pi/12,-pi/120));
Color 6;
Expr x=0;
Text "Field from instantaneous position of charge:";
Expr function(Y_i,x,A)=[if(function(Y,x,function(m,A),function(b,n)),min([function(X_b,n,A),function(X_B,n,A)])<x<max([function(X_b,n,A),function(X_B,n,A)]))];
Color 6;
Expr function(Y_i,x,T),in(T,set([-5]*pi/12,[-4]*pi/12,[-3]*pi/12,[-2]*pi/12,[-1]*pi/12,1*pi/12,2*pi/12,3*pi/12,4*pi/12,5*pi/12,-pi/120));
Text "What initially seems like the right thing is not transverse:";
Color 17;
Expr function(Y,x,function(m,pi/4),function(b,n-x/(c*cos(pi/4)))),0<x<function(X_O,n);
Text "Transverse wavefront by hand; B is the y-intercept of and Xb/B the intersection point with the transverse wave front.  (B changes sign for x><<0, so Xb changes as well.)   Some of the extraneous definitions (Xo,BB) are because GC chokes on putting - signs in conditionals arg lists -- bug.";
Color 4;
Expr function(B,s,A)=function(Y_O,s,A)+1/function(m,A)*function(X_O,s,A);
Color 8;
Expr function(B_B,s,A)=-[function(Y_O,s,A)+1/function(m,A)*function(X_O,s,A)];
Color 2;
Expr function(X_b,s,A)=[function(B,s,A)-function(b,s)]*sin([2*A])/2;
Color 7;
Expr function(X_B,s,A)=[-[function(B,s,A)+function(b,s)]]*sin([2*A])/2;
Color 3;
Expr function(Y_b,x,A)=[if(function(Y,x,-1/function(m,A),function(B,n,A)),min([function(X_b,n,A),function(X_O,n,A)])<x<max([function(X_b,n,A),function(X_O,n,A)]))];
Color 3;
Expr function(Y_B,x,A)=[if(function(Y,x,-1/function(m,A),function(B_B,n,A)),min([function(X_B,n,A),function(X_o,n,A)])<x<max([function(X_B,n,A),function(X_o,n,A)]))];
Color 2;
Expr function(Y_b,x,T),in(T,set([-5]*pi/12,[-4]*pi/12,[-3]*pi/12,[-2]*pi/12,[-1]*pi/12,1*pi/12,2*pi/12,3*pi/12,4*pi/12,5*pi/12,-pi/120));
Color 2;
Expr function(Y_B,x,T),in(T,set([-5]*pi/12,[-4]*pi/12,[-3]*pi/12,[-2]*pi/12,[-1]*pi/12,1*pi/12,2*pi/12,3*pi/12,4*pi/12,5*pi/12,-pi/120));
Text "

<size=16>Author: David A. Craig <<http://web.lemoyne.edu/~craigda/>";