A customer working with RFID devices asked me about finding magnetic flux inside a detector coil surrounded by an array of drive coils. The drive coils may move around or rotate. There are no iron structures. The calculations are fast and easy using the free-space mode of **Magnum**. In this post, I’ll review the required techniques.

The first figure shows a test geometry. The detector coil has a rectangular cross section (Δ*x* = 6.0 cm, Δ*y* = 3.5 cm). For convenience, I located it in the plane *z* = 0.00 cm. I included one circular drive coil of radius 5.0 cm with center at (*x* = 5.0 cm, *y* = 5.0 cm and *z* = 5.0). To illustrate parameter variations, I rotated it 45° around the *x* axis. Here is the coil definition file created in **MagWinder**:

GLOBAL

DUnit: 1.0000E+02

END

COIL

Name: RotatingCoil

Current: 1.0000E+00

Ds: 2.5000E-01

Shift: 5.0000E+00 5.0000E+00 5.0000E+00

Part

Name: RotatingCoil

Type: Circle

Fab: 5.0000E+00

* Change ThetaX to rotate the coil

Rotate: 45.000 0.000 0.000 XYZ

End

END

ENDFILE

The coil can be rotated by editing the part in **Magwinder **or simply changing the value 45.000 with a text editor. The coil definition file is processed with **Magwinder **to create a list of 126 short current elements to calculate the applied field at the position of the diagnostic coil.

In a **Magnum **free space solution, the computational mesh defines a set of node points to calculate the applied field. The field at other points is determined by interpolation. All elements have μr = 1.0. Usually, the mesh is a single-region box that surrounds the volume of interest. In this case, I used a special region division to enable automatic flux calculations. The figure below shows the mesh, extending over a range that encloses the detector coil (-5.0 ≤ *x* ≤ 5.0, -5.0 ≤ *y* ≤ 5.0, -1.0 ≤ *z* ≤ 1.0). The upper and lower spaces in *z* are divided into Region 1 and 2. Region 3 occupies the lower space in *z* and has the cross-section dimensions of the detector coil (Δ*x* = 6.0 cm, Δ*y* = 3.5 cm). The important point is that the surface between Region 3 and 1 corresponds to the area enclosed by the detector coil.

The **Magnum **solution takes only a few seconds. **MagView **is then used to analyze the solution. To calculate the flux integral, click on A*nalysis/Surface integral* to show the dialog illustrated below. We want to find the flux out of Region 3 into Region 1 (*i.e.*, a positive value corresponds to *Bz* > 0.0). Therefore, we set the dialog so that Region 3 is internal and Region 1 is external. The program determines integrals over the defined surface and records the results in a data file (shown below):

———- Surface Integrals ———-

Region status

RegNo Status Name

===================================

1 External AIRUPPER

3 Internal COILOUTLINE

Surface area of region set (m2): 2.100000E-03

MagFlux: -2.537678E-09

As a check, we confirm that the area equals 0.060 m × 0.035 m. The flux implies an average flux density <*Bz*> = 1.208E-6 tesla. Inspection of a plot of *Bz* in the plane *z* = 0.0 cm shows that this is a reasonable value.

For more information on **Magnum**, please see http://www.fieldp.com/magnum.html. For program users, here are links to the example input files:

http://www.fieldp.com/myblog/examples/MagneticFlux.CDF

http://www.fieldp.com/myblog/examples/MagneticFlux.MIN

http://www.fieldp.com/myblog/examples/MagneticFlux.GIN