GraphingCalculator 4;
Window 45 6 831 1372;
PaneDivider 447;
FontSizes 14;
BackgroundType 0;
BackgroundColor 255 255 255;
StackPanes 1;
3D.Axes 0;
3D.Depth 1.5830909743;
3D.View 0.5376841184333139 -0.8040302816936172 -0.2538328090656449 0.7239576594432021 0.5945726247721819 -0.3498123800825449 0.4321817860256187 0.004324354860567546 0.9017761384271846;
3D.Speed 0;
Text "Coulomb and Biot-Savart Laws.

Version 0.25 11-16-15
To do:
(i) Other source currents
(ii) This seems a little slower defined in terms of V and A than original (versions 0.25 and previous) directly in terms of derivatives of X.


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 82;
Expr A_0=slider([0,10]);
Color 6;
MathPaneSlider 96;
Expr p=slider([0,1]);
Color 4;
Expr function(f,x)=A_0*cos(x),function(g,x)=A_0*sin(x),function(h,x)=p*x;
Color 3;
Expr function(X,t)=vector(function(f,t),function(g,t),function(h,t));
Color 3;
Expr function(V,t)=function(oppartial(t),function(X,t));
Color 8;
Expr function(A,t)=function(oppartial(t),function(V,t));
Color 5;
Expr function(T,t)=function(V,t)/abs(function(V,t));
Color 7;
Expr function(N,t)=(function(A,t)-([dot(function(A,t),function(T,t))]*function(T,t)))/abs(function(A,t)-([dot(function(A,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);
Color 8;
MathPaneSlider 88;
Expr W=slider([0,0.05]);
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 74;
Expr d=slider([0,1]);
Color 4;
Expr function(D,t)=function(T,t)*d;
Color 7;
MathPaneSlider 104;
Expr s=slider([-10,10]);
Expr function(X,s+d*t/abs(function(V,s)));
Color 17;
Expr function(X,s),function(X,s)+function(D,s),'radius'=W;
Color 17;
Expr function(X,s),function(X,s)+function(V,s),'radius'=W;
Color 17;
Expr function(X,s),function(X,s)+function(N,s),'radius'=W;
Text "Absolute field point F:";
Color 8;
MathPaneSlider 123;
Expr a=slider([-10,10]);
Color 2;
MathPaneSlider 99;
Expr b=slider([-10,10]);
Color 3;
MathPaneSlider 99;
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 93;
Expr h=slider([0,pi]);
Color 2;
MathPaneSlider 178;
Expr k=slider([0,2*pi]);
Color 4;
MathPaneSlider 126;
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 17;
Expr function(X,s),function(X,s)+R,'radius'=W;
Color 17;
Expr function(X,s)+R,function(X,s)+R+function(B,s),'radius'=W;
Text "To aid in visualizing Biot-Savart Law:";
Color 17;
Expr function(X,s)+function(N,s)*l*sin([h])*cos([2*pi*t])+function(M,s)*l*sin([h])*sin([2*pi*t])+function(T,s)*l*cos([h]);
Color 17;
Expr function(X,s)+10*[t-1/2]*function(T,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),'radius'=W;
Text "

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