# Unmapped white region in ContourPlot, PlotRange -> All does not fix the issue

When I try to create a ContourPlot of the magnitude of the following vector I get a white area that should be filled with values.

Running the following code:

Bx := 0
By[y_, z_] := (\[Mu]0*j*(y - dy))/(2*Pi ((y - dy)^2 + (z - dz)^2))
Bz[y_, z_] := (\[Mu]0*j*(z - dz))/(2*Pi ((y - dy)^2 + (z - dz)^2))

bwi3D[y_, z_] := {Bx, By[y, z], Bz[y, z]}

bb3Dz = {0, 0, -(\[Mu]0*j)/(2 Pi 5 10^-6)}

const = {\[Mu]0 -> 4 Pi*10^-7, \[Chi] -> -4.5 *10^-4};

params = {j -> 5, V -> (25*10^-18), dz -> 0, dy -> 0};

b3Dz[y_, z_] := bwi3D[y, z] + bb3Dz /. const /. params

ContourPlot[Sqrt[(b3Dz[y, z][] /. const /. params)^2 + (b3Dz[y, z][] /. const /.params)^2],
{y, -10 (10^-6), 10*(10^-6)}, {z, -10 (10^-6), 10*(10^-6)},
ColorFunction -> "Rainbow", Contours -> 100, FrameLabel -> {"y (m)", "z (m)"},
PlotLabel -> "Contour of field magnitude with z bias"]


I get a contour that looks like this: Zooming in reveals contours in regions that were previously engulfed in this white area and using PlotRange -> All results in the following monstrosity: I think this issue is tied to the fact that there is a singularity in this function at y=0 and z=0, but I don't know how to exclude this point. I also have no clue why PlotRange->All is resulting in an all purple plot.

Any help would be appreciated.

Edit: Thanks for bearing with me while I added all the code and fixed the formatting

• Hi Bob, here is some more code: Bx := 0 By[y_, z_] := (\[Mu]0*j*(y - dy))/(2*Pi ((y - dy)^2 + (z - dz)^2)) Bz[y_, z_] := (\[Mu]0*j*(z - dz))/(2*Pi ((y - dy)^2 + (z - dz)^2)) bwi3D[y_, z_] := {Bx, By[y, z], Bz[y, z]} const = {\[Mu]0 -> 4 Pi*10^-7, \[Chi] -> -4.5 *10^-4}; params = {j -> 5, V -> (25*10^-18), dz -> 0, dy -> 0}; b3Dz[y_, z_] := bwi3D[y, z] + bb3Dz /. const /. params I think this should be enough to reproduce this code? Also it doesn't recognise Clipping as a function. Thank you for your reply. – Amir Arshad Nov 14 '14 at 17:09
• @AmirArshad Hi ! Please, add this to your original post to make it a complete question. – Sektor Nov 14 '14 at 17:11
• Sure, no problem. – Amir Arshad Nov 14 '14 at 17:12
• I think everything should be there guys. Sorry for taking so long! – Amir Arshad Nov 14 '14 at 17:18

Bx = 0;
By[y_, z_] = (\[Mu]0*j*(y - dy))/(2*Pi ((y - dy)^2 + (z - dz)^2));
Bz[y_, z_] = (\[Mu]0*j*(z - dz))/(2*Pi ((y - dy)^2 + (z - dz)^2));

bwi3D[y_, z_] = {Bx, By[y, z], Bz[y, z]};

bb3Dz = {0, 0, -(\[Mu]0*j)/(2 Pi 5 10^-6)};

const = {\[Mu]0 -> 4 Pi*10^-7, \[Chi] -> -4.5*10^-4};

params = {j -> 5, V -> (25*10^-18), dz -> 0, dy -> 0};

b3Dz[y_, z_] = bwi3D[y, z] + bb3Dz /. const /. params;

Manipulate[
ContourPlot[
Sqrt[(b3Dz[y, z][] /. const /. params)^2 +
(b3Dz[y, z][] /. const /. params)^2],
{y, -10 (10^-6), 10*(10^-6)},
{z, -10 (10^-6), 10*(10^-6)},
ColorFunction -> "Rainbow", Contours -> 100,
FrameLabel -> {"y (m)", "z (m)"},
PlotLabel -> "Contour of field magnitude with z bias",
ClippingStyle -> Automatic,
PlotRange -> {0, maxPeak}],
{{maxPeak, .6}, .5, 5, .1, Appearance -> "Labeled"},
SynchronousUpdating -> False] As the PlotRange is increased the contours get pulled closer around the peak and there is little relative variation in the majority of the plot.

• Thanks for this. For my project the more important area is the minimum which is located at z=5x10^-6 but I just wanted to understand what this white region was and how i could demonstrate what was going on. This Manipulation of the contours is great. Thanks for your time. – Amir Arshad Nov 14 '14 at 17:56