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):
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
.
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.
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:
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:
To be able to display the variation of the magnetic field along the axis of the Toroid, before running the simulation:
Once the simulation is complete:
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
Figure 5 - Section plot of the magnetic flux density