# Question:Empty box using fieldplot3d function

## Question:Empty box using fieldplot3d function

Maple 18

Hello;

I am trying to verify the analytic solution of a electric and magnetic fields created by a small dipole antenna (also called "Hertzian dipole"). The study of a small dipole is ground zero of anyone learning about antennas as calculations are "relatively" easy if a mathematical software is used. As the title suggests, the fieldplot3d returns an empty box.

Here is some introduction for the problem in question:

The procedure is relatively straightforward, first, current density vector is defined, from there, magnetic vector potential (named "vector A") is calculated. The curl of vector A gives the magnetic field (named "B-field") produced by the antenna. From B-field, H field is deduced as it is only a multiplication of the B-field by a constant.

At this point, I try to plot the H-field, and it works like a charm. No problem at all.

The electric field (named "E-field") then, may be calculated by taking the curl of the H-field and multiplying by a constant.

At this second point, I try to plot the E-field, however, Maple returns an empty box.

First, I thaught, maybe it was a problem of division by 0, however, after redefining the axis ranges, the problem still persists. I am attaching the code and the images. Any help will be greatly appreciated.

PS: This is my first post and I am very new to maple, please indulgde me if I make some formatting and/or post mistakes

KB

First step: Verify calculations for Hertzian dipole

 > restart;
 > with(plots):
 > with(LinearAlgebra):
 > with(VectorCalculus):
 > #IMPORTANT: R is constant for the calculation of A
 >
 >
 >
 >
 > J:=Vector[column]([ 0 ,                  0 ,                  I_0/s ]);
 (1)
 >
 >
 (2)
 > A[1];
 (3)
 > A[2];
 (4)
 > A[3];
 (5)
 > #Taking the curl of A:
 > #IMPORTANT: R is a function of x,y,z:
 > R:=sqrt(x^2+y^2+z^2);
 (6)
 >
 >
 >
 > #Defining B by taking the curl
 >
 >
 >
 >
 >
 >
 >
 > B:=Vector[column]([ B[1] ,                  B[2] ,                  B[3] ]):

 > mu_0:=4*Pi*10^(-7):
 > I_0:=2400:
 > f:=2500:
 > omega:=2*Pi*f:
 > c:=3*10^8:
 > k:=omega/c:
 > l:=3*10^(-2):
 > epsilon_0:=1/(mu_0*c^2):

 > B_plot:=fieldplot3d([B[1],B[2],B[3]], x=-1..1,y=-1..1,z=-1..1,fieldstrength=log,arrows=SLIM):

 > H:=(1/mu_0)*B:
 >
 > H_plot:=fieldplot3d([H[1],H[2],H[3]], x=-1..1,y=-1..1,z=-1..1,fieldstrength=log,arrows=SLIM):
 >
 > # Taking curl of H to find the E field:
 >
 >
 >
 >
 > E:=Vector[column]([ E[1] ,                  E[2] ,                  E[3] ]):
 > E_plot:=fieldplot3d([E[1],E[2],E[3]], x=1..500,y=1..500,z=1..500,fieldstrength=log,arrows=SLIM):
 >
 >
 > subs(x=1,y=1,z=1,H):
 >
 > H_plot;
 >
 >
 > E_plot;
 >

﻿