What is returned by "FlowData" in pdeplot?

Good day!

I can't understand what parameter is returned by

pdeplot(emagmodel,"FlowData",[R.MagneticField.Hx,R.MagneticField.Hy],"Contour","on","FaceAlpha",0.9)

when solving

emagmodel = createpde("electromagnetic","magnetostatic");

The parameter "FlowData" adds arrows to the picture, but what is a physical meaning of these arrows? Its name is "field", but what does it means?? Is in an Inductance B, in Tesla? Magnetic field strength H , in Ampere/meter? In any cases, why do it is greater outside the magnetic conductor and becomes much smaller inside the magnetic conductor?

https://fr.mathworks.com/help/pde/ug/magnetic-field-in-two-pole-electric-motor.html

Answer 1

[Swaraj]

Hi,

I understand that you want to know about the “FlowData” in context of “pdeplot”.

pdeplot() returns a handle to a plot. “FlowData” represents the data for the “quiver plot”, specified as an M-by-2 matrix, where M is the number of mesh nodes. “FlowData” contains the x and y values of the field at the mesh points.

A quiver plot is a plot of a vector field. It is also called a flow plot.The arrows which are present in the final plot shared shows the direction of the field, with the lengths of the arrows showing the relative sizes of the field strength.

The magnetic field strength (H) is related to the magnetic flux density (B) by the permeability of the material being analysed, which is a measure of how easily the material can be magnetized. In magnetic conductors, the permeability is higher, which means that the magnetic field strength is higher, while in non-magnetic materials, the permeability is lower, which means that the magnetic field strength is lower.

In the example you mentioned, in the final graph, actually the magnetic flux lines are more concentrated in the conductor. Outside the conductor, the magnetic field lines spread out more, and the magnetic field strength decreases as the distance from the conductor increases. This is because the air has a lower magnetic permeability than the conductor, so the magnetic field lines are more spread out in the air.

The following documentations might help as well.

Plot solution or mesh for 2-D problem - MATLAB pdeplot (mathworks.com)

Quiver or vector plot - MATLAB quiver (mathworks.com)

Hope this clarifies your doubts!

[Deniss]

Ok, so this option is only to show the magnetic field pattern not in color, but in quiver (same info with different representation) and it can be called from the PDE MOdeller or from a script through "FlowData".

But is it possible to display the magnetic flux density B from the command window? Yes, itt is possible to do this from the PDE Modeller ( https://www.mathworks.com/help/pde/ug/magnetostatics.html last illustration), but is it possible to command to display B from the script (command window)?