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

Question

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][[2]] /. const /. params)^2 + (b3Dz[y, z][[3]] /. 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

Answer 1

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][[2]] /. const /. params)^2 +
    (b3Dz[y, z][[3]] /. 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.