Hello everyone!

I am confronted with a problem that seems to result from different definition of spherical coordinates in Maple and in **Student[VectorCalculus]** package.

I want to visualize a vector field defined in __spherical coordinates (r,theta,phi)__.

A simple exampe is < 0, theta, 0 >. If I want to see just one slice of the field in OXY plane, I type:

**fieldplot3d(<0, theta, 0>, r = 0 .. 1, theta = 0 .. 2*Pi, phi = 0 .. Pi, coords = spherical, grid = [10, 20, 3], color = black, fieldstrength = fixed(1), arrows = THICK)**

And get:

which looks OK more or less but I don't like the nonuniform distribution of arrows. But since the field is defined in spherical coordinates there seems to be no way to produce a uniform distribution with **fieldplot3d** command.

However **VectorField **command in** Student[VectorCalculus]** package seems to do just what I want. But a similar call to it:

**SetCoordinates('spherical'[r, theta, phi])**

**VectorField(<0, theta, 0>, output = plot, view = [-5 .. 5, -5 .. 5, -10 .. 10], fieldoptions = [arrows = THICK, color = black, grid = [10, 10, 3], view = [-5 .. 5, -5 .. 5, -1 .. 1]])** produces quite a different result:

which means that the second argument 'theta' is not the azimuthal angle but the angle from the Z axis, and amounts to Pi/2 since we look at the OXY plane.

The result of: **VectorField(<0, 0, theta>, output = plot, view = [-5 .. 5, -5 .. 5, -10 .. 10], fieldoptions = [arrows = THICK, color = black, grid = [10, 10, 3], view = [-5 .. 5, -5 .. 5, -1 .. 1]])** looks better:

but is not correct since the magnitude of the field does not change with the azimutal angle. Finally,

**VectorField(<0, 0, phi>, output = plot, view = [-5 .. 5, -5 .. 5, -10 .. 10], fieldoptions = [arrows = THICK, color = black, grid = [10, 10, 3], view = [-5 .. 5, -5 .. 5, -1 .. 1]]) **produces almost what I want:

but it's quite different from what you get with **fieldplot3d** command. Apparently, not only azimuthal angle is now the third argument but it varies from -Pi to Pi, not from 0 to 2Pi as it does in **fieldplot3d.** I hoped to use both **fieldplot3d** and **VectorField ** with my vector fields but I cannot since they are not consistent in the definition of spherical coordinates.

My questions therefore are:

1) Is there a way to redifine spherical coordinates in **VectorField **command to make them consistent with the rest of Maple?

2) Can I produce a uniform 3D distribution of arrows for a field in spherical coordinates without **VectorField **command?

Many thanks for your help in advance!