3D dipole antenna pattern corresponding to simple linear antenna.

To do:
(i) Physically accurate field strengths
(ii) Solid angle slows things down considerably at higher resolutions...

Larmor formula: P=(2/3)(qa)^2/c^3; dP/d\Omega = (1/4pi)(qa)^2/c^3sin^2(theta).

a^2*[sin(phi)]^2=r

Acceleration of source charge:

a=slider([0,1])

-(a/2*K),a/2*K

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

q=slider([0,1])

p=slider([0,1])

T=pi*q,P=2*pi*p

function(R_h,T,P)=vector(sin(T)*cos(P),sin(T)*sin(P),cos(T)),function(T_h,T,P)=vector(cos(T)*cos(P),cos(T)*sin(P),-sin(T)),function(P_h,T,P)=vector(-sin(P),cos(P),0)

function(X,R,T,P)=vector(R*sin(T)*cos(P),R*sin(T)*sin(P),R*cos(T))

Electric field strength goes like (e/c)(a*sinT/r). (E is proportional to Xcross(Xcrossa).) Exhibit just angular dependence (f is a visibility scale factor):

E=f*a*sin(T)

f=slider([0,1])

R=a^2*sin(T)^2+0.1

Electric and magnetic field directions and Poynting vector (R,G,Y):

function(X,R,T,P),function(X,R,T,P)+function(T_h,T,P)*E

function(X,R,T,P),function(X,R,T,P)+function(P_h,T,P)*E

function(X,R,T,P),function(X,R,T,P)+function(R_h,T,P)*E^2/f^2

function(X,R,T,P)

O,function(X,R,T,P)

Solid angle around observation direction. (Higher resolution slows down plotting to a crawl, so don't try smaller opening angles at high resolution until observation direction has been set.)

c=slider([0,0.1])

C=pi*c

cos(C)=dot(vector(x,y,z),function(R_h,T,P))/sqrt(x^2+y^2+z^2),r<R+0.1*s




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

Graph of the formula

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