GraphingCalculator 3.5;
Window 46 6 830 760;
PaneDivider 408;
FontSizes 14 12 10;
BackgroundType 0;
BackgroundColor 255 255 255;
3D.X -1 1;
3D.Y -1 1;
3D.Z -1 1;
3D.Axes 0;
3D.View 0.561986654341702 -0.8025679095849844 -0.200139328677698 0.7658538696444105 0.5962879435447941 -0.2406419306172391 0.3124721599278418 -0.0180399258536005 0.9497556056073511;
3D.Speed 0;
Text "Coulomb and Biot-Savart Laws.

Version 0.1 11-2-08
To do:
(i) Other source currents


Permittivity, permeability, current and/or linear charge density.";
Expr e_0=1,U_0=1;
Color 2;
MathPaneSlider 200;
Expr j=slider([-40,40]);
Text "Current path X and its Frenet vectors: the unit tangent T, normal N and binormal M.  

For now, a spiral with variable radius and pitch.";
Color 5;
MathPaneSlider 65;
Expr A=slider([0,10]);
Color 6;
MathPaneSlider 8;
Expr p=slider([0,1]);
Color 4;
Expr function(f,x)=A*cos(x),function(g,x)=A*sin(x),function(h,x)=p*x;
Color 3;
Expr function(X,t)=vector(function(f,t),function(g,t),function(h,t));
Color 5;
Expr function(T,t)=1/abs(function(oppartial(t),function(X,t)))*[function(oppartial(t),function(X,t))];
Color 7;
Expr function(N,t)=(function(oppartial(t),function(oppartial(t),function(X,t)))-([dot([function(oppartial(t),function(oppartial(t),function(X,t)))],function(T,t))]*function(T,t)))/abs(function(oppartial(t),function(oppartial(t),function(X,t)))-([dot([function(oppartial(t),function(oppartial(t),function(X,t)))],function(T,t))]*function(T,t)));
Color 8;
Expr function(M,t)=cross(function(N,t),function(T,t))/abs(cross(function(N,t),function(T,t)));
Color 6;
Expr O=vector(0,0,0),I=vector(1,0,0),J=vector(0,1,0),K=vector(0,0,1);
Text "Source current:";
Color 5;
MathPaneSlider 200;
Expr S=slider([0,10]);
Color 6;
Expr function(X,S*t);
Text "Source segment:";
Color 3;
MathPaneSlider 22;
Expr d=slider([0,1]);
Color 4;
Expr function(D,t)=function(T,t)*d;
Color 7;
MathPaneSlider 103;
Expr s=slider([-10,10]);
Expr function(X,s+d*t);
Color 2;
Expr function(X,s),function(X,s)+function(D,s);
Color 17;
Expr function(X,s),function(X,s)+function(N,s);
Text "Absolute field point F:";
Color 8;
MathPaneSlider 116;
Expr a=slider([-10,10]);
Color 2;
MathPaneSlider 114;
Expr b=slider([-10,10]);
Color 3;
MathPaneSlider 100;
Expr c=slider([-10,10]);
Color 7;
Expr F=vector(a,b,c);
Text "Field point relative to X(s) [h,k,l are like spherical theta, phi, r relative to the curve's Frenet vectors T,N,E]:";
MathPaneSlider 111;
Expr h=slider([0,pi]);
Color 2;
MathPaneSlider 189;
Expr k=slider([0,2*pi]);
Color 4;
MathPaneSlider 95;
Expr l=slider([0,2]);
Color 4;
Expr function(Y,t)=function(N,t)*l*sin([h])*cos([k])+function(M,t)*l*sin([h])*sin([k])+function(T,t)*l*cos([h]);
Text "Field point R relative to X(s) – specified absolutely if q=0 and relative to X(s) if q=1:";
Color 6;
MathPaneSlider 1;
Expr q=slider([0,1,1]);
Color 7;
Expr R=[F-function(X,s)]*[1-q]+function(Y,s)*q;
Text "Magnetic Field due to source segment at field point:";
Expr function(B,s)=U_0*j/(4*pi)*cross(function(D,s),R)/abs(R)^3;
Color 8;
Expr function(X,s),function(X,s)+R;
Color 3;
Expr function(X,s)+R,function(X,s)+R+function(B,s);
Text "Electric Field due to source segment at field point:";
Color 5;
Expr function(E,s)=1/(4*pi*e_0)*j*d/abs(R)^3*R;
Color 17;
Expr function(X,s)+R,function(X,s)+R+function(E,s);
Text "

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