(*^
::[	Information =

	"This is a Mathematica Notebook file.  It contains ASCII text, and can be
	transferred by email, ftp, or other text-file transfer utility.  It should
	be read or edited using a copy of Mathematica or MathReader.  If you 
	received this as email, use your mail application or copy/paste to save 
	everything from the line containing (*^ down to the line containing ^*)
	into a plain text file.  On some systems you may have to give the file a 
	name ending with ".ma" to allow Mathematica to recognize it as a Notebook.
	The line below identifies what version of Mathematica created this file,
	but it can be opened using any other version as well.";

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:[font = section; inactive; initialization; preserveAspect; cellOutline; backColorRed = 58981; backColorGreen = 58981; backColorBlue = 58981]
Your Assignment:
1) Execute the entire notebook.  Experiment if you like. 
2) Generate a plot for the set of 3 charges described at the end.
3) Hand in the plot.
;[s]
2:0,0;16,1;162,-1;
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 Suggestion: if you want to save this file on you disk, CUT the graphics first so it will fit. (Graphics take up over 1MB.)
:[font = section; inactive; initialization; Cclosed; preserveAspect; startGroup]
**********************************
Initialization Stuff:
(Just execute this, don't read it!!!)
;[s]
2:0,0;56,1;95,-1;
2:1,19,14,Times,1,18,0,0,0;1,16,12,Times,1,14,0,0,0;
:[font = input; initialization; preserveAspect]
*)
Needs["Graphics`PlotField`"];
Needs["Graphics`PlotField3D`"];
(*
:[font = subsubsection; inactive; initialization; preserveAspect]
Don't mind any   Warning:... ind an messages here!
;[s]
3:0,0;16,1;29,0;51,-1;
2:2,13,9,Times,1,12,0,0,0;1,13,10,Courier,0,12,65535,0,0;
:[font = input; initialization; preserveAspect]
*)
Clear["Global`*"];

Monopole[q_,v0_:{0,0,0},v_:{x,y,z}]:= q/(Sqrt[(v0-v).(v0-v)])
(*
:[font = input; initialization; preserveAspect]
*)
go2d[distribution_]:=
 PlotGradientField[-distribution/.{z->0} //Evaluate 
    ,{x,-2,2.01},{y,-2,2.01}
    ,Graphics`PlotField`ScaleFunction->(1&)];
(*
:[font = input; initialization; preserveAspect]
*)
go3d[distribution_]:=
 PlotGradientField3D[-distribution  //Evaluate 
    ,{x,-2,2.01},{y,-2,2.01},{z,-2,2.01}
    ,PlotPoints->8
    ,Graphics`PlotField3D`ScaleFunction->(1&)
    ,VectorHeads->True];
(*
:[font = input; initialization; preserveAspect; endGroup]
*)
Protect[{go2d,go3d,Monopole}];
Off[Clear::wrsym];
(*
:[font = section; inactive; preserveAspect; cellOutline; backColorRed = 58981; backColorGreen = 58981; backColorBlue = 58981]
**********************************
Electric Fields Due to Point Charges:
:[font = input; preserveAspect]
Clear["Global`*"];
:[font = text; inactive; preserveAspect]
 The Monopole[q,{x,y,z}] function places a single charge q 
  at position {x,y,z}.  An example would be:  Monopole[+1,{1,0,0}]
Let's look at the field due to a single charge located at the origin, {x,y,z}={0,0,0}. 

The function go2d automatically plots the electric field vector in the {x,y} plane. 
(This automatically plots the region from {-2,2}.)
;[s]
5:0,0;105,1;127,0;229,1;233,0;352,-1;
2:3,13,9,Times,0,12,0,0,0;2,13,10,Courier,1,12,0,0,0;
:[font = input; preserveAspect]
go2d[ Monopole[+1,{0,0,0}] ];
:[font = text; inactive; preserveAspect]
We can create a dipole from two Monopole functions:
(Notice that the signs are opposite)
;[s]
3:0,0;32,1;40,0;89,-1;
2:2,13,9,Times,0,12,0,0,0;1,13,10,Courier,1,12,0,0,0;
:[font = input; preserveAspect]
dipole= Monopole[+1,{1,0,0}]+Monopole[-1,{-1,0,0}]
:[font = text; inactive; preserveAspect]
Now let's look at the E field.
:[font = input; preserveAspect]
go2d[ dipole ];
:[font = text; inactive; preserveAspect]
In a similar fashion, go3d makes a plot of the E field in 3-dimensions. Try it! (3D plots will take some time.)
;[s]
5:0,0;22,2;26,0;80,1;111,0;112,-1;
3:3,13,9,Times,0,12,0,0,0;1,13,9,Times,3,12,0,0,0;1,13,10,Courier,1,12,0,0,0;
:[font = input; preserveAspect]
thisPlot= go3d[ dipole ];
:[font = text; inactive; preserveAspect]
This may look neater from a different viewpoint. 
(Note how I defined thisPlot so I would not have to re-compute the above plot. This saves time.)
(3D plots will take some time.)
;[s]
3:0,0;147,2;178,1;179,-1;
3:1,13,9,Times,0,12,0,0,0;1,13,9,Times,3,12,0,0,0;1,13,9,Times,1,12,0,0,0;
:[font = input; preserveAspect]
Show[thisPlot,ViewPoint->{0.000, 0.000, 4.000}];
:[font = text; inactive; preserveAspect]
Now you get the idea. Instead of a dipole, let's try two charges of the same sign. 
:[font = input; preserveAspect]
twoCharges= Monopole[+1,{1,0,0}]+Monopole[+1,{-1,0,0}]
:[font = input; preserveAspect]
go2d[ twoCharges ];
:[font = subsection; inactive; preserveAspect; cellOutline; backColorRed = 58981; backColorGreen = 58981; backColorBlue = 58981]
Now that you are started, you can experiment with different charge configurations. Try three charges located at {1,0,0}, {-1,0,0}, {0,1,0}.  Go and experiment. 
^*)