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MathGroup Archive 2007

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Re: Manipulate a VectorFieldPlot3D

  • To: mathgroup at smc.vnet.net
  • Subject: [mg80501] Re: Manipulate a VectorFieldPlot3D
  • From: Albert <awnl at arcor.net>
  • Date: Thu, 23 Aug 2007 06:24:09 -0400 (EDT)
  • References: <faj4u1$8rp$1@smc.vnet.net>

Hi,

> I would like to 3D plot two time dependent fields E and B.
> I have two questions about the current state of my notebook:
> 
>  Why the options Axes and AxesLabel produce an error, while producing
> the expected behaviour (adding the axes label!)
> 
>  How can I have a Manipulate object that would allow me to scan over time?

The following code works for me. Since the generation of the plots is 
somewhat lengthy I used the option ContinousAction->False for 
Manipulate. As has already been explained in this group thath it seems 
to be the best approach to define functions of the variables you want to 
Manipulate. This way there is no need for explicit usage of Dynamic 
anywhere...

Clear["Global`*"]
<<PhysicalConstants`
Needs["VectorFieldPlots`"]
c=299792458;(*SpeedOfLight*)
\[Mu]=\[Pi]/2500000;(*VacuumPermeability*)
\[Epsilon]=8.854187817`*^-12;(*VacuumPermittivity*)
\[Omega]=1;(*Angular speed*)
p=1;(*Unit dipole moment*)
k=\[Omega]/c;(*Norm of the wave vector*)
r=Norm[{x,y,z}];(*Norm of the position vector*)
a=10;
Ex[t_]=(y^2+z^2) Cos[\[Omega] t-k r]-x y Sin[\[Omega] t-k r];
Ey[t_]=(x^2+z^2) Sin[\[Omega] t-k r]-x y Cos[\[Omega] t-k r];
Ez[t_]=z (x Cos[\[Omega] t-k r]+y Sin[\[Omega] t-k r]);
Bx[t_]=-z Sin[\[Omega] t-k r];
By[t_]=z Cos[\[Omega] t-k r];
Bz[t_]=x Sin[\[Omega] t-k r]-y Cos[\[Omega] t-k r];
Manipulate[
Column[{
Row[{"time = ",t}],
Row[{
Show[
VectorFieldPlot3D[(\[Omega]^2 p/4 \[Pi] \[Epsilon] c^2 r^3) 
{Ex[t],Ey[t],Ez[t]},{x,-a,a},{y,-a,a},{z,-a,a},VectorHeads->True],
Axes->True,AxesLabel->{x,y,z},PlotLabel->"E",ImageSize->300
],
Show[
VectorFieldPlot3D[(\[Mu] \[Omega]^2 p/4 \[Pi] c r^2) 
{Bx[t],By[t],Bz[t]},{x,-a,a},{y,-a,a},{z,-a,a},VectorHeads->True],
Axes->True,AxesLabel->{x,y,z},PlotLabel->"B",ImageSize->300
]
}]
}],
{t,0,100},
ContinuousAction->False
]

For this case I probably would prefer to visualize the time dependency 
with something like:

With[{c1 = (\[Omega]^2 p/4 \[Pi] \[Epsilon] c^2 r^3),
    c2 = (\[Mu] \[Omega]^2 p/4 \[Pi] c r^2)},
   graphlist = Table[
     PrintTemporary[t];
     Column[{
       Row[{"time = ", t}],
       Row[{
         Show[
          VectorFieldPlot3D[
           c1 {Ex[t], Ey[t], Ez[t]}, {x, -a, a}, {y, -a, a}, {z, -a,
            a}, VectorHeads -> True], Axes -> True,
          AxesLabel -> {x, y, z}, PlotLabel -> "E", ImageSize -> 300,
          PlotRange -> {{-a, a}, {-a, a}, {-a, a}}
          ],
         Show[
          VectorFieldPlot3D[
           c2 {Bx[t], By[t], Bz[t]}, {x, -a, a}, {y, -a, a}, {z, -a,
            a}, VectorHeads -> True], Axes -> True,
          AxesLabel -> {x, y, z}, PlotLabel -> "B", ImageSize -> 300,
          PlotRange -> {{-a, a}, {-a, a}, {-a, a}}
          ]
         }]
       }],
     {t, 0, 100, 10}
     ]
   ];

ListAnimate[graphlist]

hth,

albert


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