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.

e_0=1,U_0=1

j=slider([-40,40])

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.

A=slider([0,10])

p=slider([0,1])

function(f,x)=A*cos(x),function(g,x)=A*sin(x),function(h,x)=p*x

function(X,t)=vector(function(f,t),function(g,t),function(h,t))

function(T,t)=1/abs(function(oppartial(t),function(X,t)))*[function(oppartial(t),function(X,t))]

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)))

function(M,t)=cross(function(N,t),function(T,t))/abs(cross(function(N,t),function(T,t)))

O=vector(0,0,0),I=vector(1,0,0),J=vector(0,1,0),K=vector(0,0,1)

Source current:

S=slider([0,10])

function(X,S*t)

Source segment:

d=slider([0,1])

function(D,t)=function(T,t)*d

s=slider([-10,10])

function(X,s+d*t)

function(X,s),function(X,s)+function(D,s)

function(X,s),function(X,s)+function(N,s)

Absolute field point F:

a=slider([-10,10])

b=slider([-10,10])

c=slider([-10,10])

F=vector(a,b,c)

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]:

h=slider([0,pi])

k=slider([0,2*pi])

l=slider([0,2])

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])

Field point R relative to X(s) – specified absolutely if q=0 and relative to X(s) if q=1:

q=slider([0,1,1])

R=[F-function(X,s)]*[1-q]+function(Y,s)*q

Magnetic Field due to source segment at field point:

function(B,s)=U_0*j/(4*pi)*cross(function(D,s),R)/abs(R)^3

function(X,s),function(X,s)+R

function(X,s)+R,function(X,s)+R+function(B,s)

Electric Field due to source segment at field point:

function(E,s)=1/(4*pi*e_0)*j*d/abs(R)^3*R

function(X,s)+R,function(X,s)+R+function(E,s)



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

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