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Physics

The Biot–Savart law makes it possible to determine magnetic field produced by electric current. The law is completely general and can in principle be used for any configuration of current paths.
The law states that an infinitesimally small current carrying path produces magnetic flux density  at a distance r:

Where  is the vacuum permeability and  is the unit vector in the direction of the distance. In symmetric problems, it is possible to simplify the analysis and obtain a closed form solution. The field on the axis of a current carrying loop can be easily computed using the Biot-Savart law, due to the fact that only  axis component  of the  vector contributes to the resultant field intensity (Fig. 1):

Figure 1- Biot-Savart law and field on centerline of a current loop

The total flux density at a point on the centerline at a distance z is found by integrating the expression for  over the circumference of the loop:

For a current and loop radius , the axial magnetic field is .

Model

A thin toroid, with a cross-section area radius 5mm, and a loop radius 100mm is simulated with Magnetostatic study in EMS.  Copper is prescribed as a material to the Toroid, while air covers the rest of the assembly. To get accurate magnetic field results, it is necessary to create sufficiently large air domain.

Solid Coil

To prescribe the EMS Coil feature to the Toroid, it is necessary to have access to its cross-section surface. Therefore, the Toroid part should be split in two bodies. To do so:
 

1. Select the Toroid part in the Solidworks feature manager
2. Click Edit component  in the Solidworks Assembly tab
3. In Solidworks menu click Insert/Molds/Split
4. In the Split feature manager, select the Top Plan of the Toroid in the Trim Tools Tab and Click Cut Part
5. In the Resulting Bodies tab, Click Select all.
6. Click OK  

In the EMS feature tree, Right-click on the Coilsfolder, select Solid Coil  .
Click inside the Components or Bodies for Coils box .
Click on the (+) sign in the upper left corner of the graphics area to open the components tree.
Click on the Toroid icon.  It will appear in the Components and Solid Bodies list.
Click inside the Faces for Entry Port box  then select the entry port face.
In the Exit Port Tab, Check “Same as Entry Port“. (Figure 3)

General Properties:

1. Click on General properties tab.
2. Keep default Coil Type as a Current driven coil.
3. Type 100 in the Net current field.
4. Click OK .

Results

To be able to display the variation of the magnetic field along the axis of the Toroid, before running the simulation:

1. In the Assembly, Select the ZX plane and sketch a line going from the center of the toroid along the z axis, with a length of 100mm.
2. Then Insert/Reference geometry/Point and add a Reference point for each end of the line.
3. In the EMS feature tree, right click study  and select Update geometry .
4. Mesh and run the study. 

Once the simulation is complete:

1. In the EMS feature tree, Under Results, right click on the Magnetic Flux Density folder and select 2D Plot then choose Linear.         
2. The 2D Magnetic Flux Density Property Manager Page appears.
3.  In the Select points tab, select the start and the end points.
4. Click OK . 

The theoretical and EMS result of the magnetic flux density along the axis of the toroid are plotted in Figure 4.The agreement between the two solutions is very good.

Figure 4 - Comparison of EMS and theoretical results for magnetic flux density along the axis of a toroid

1. Under Results , right click Magnetic flux density in the EMS feature tree
2. Select 3D Vector Plot , Section Clipping .
3. Under Section Clipping tab, select one of the sections that contain the system centerline.
4. Under Vector Options tab, define size, density and shape of the vectors in the plot.                                                                                                                                                                         

Figure 5 - Section plot of the magnetic flux density