Calculating Electromagnetic Forces and Torques
Two methods are available to calculate electromagnetic forces and torques:
•
The most general method is to use the Maxwell stress tensor.
•
Another method that works for the special case of computation of magnetic forces on nonmagnetic, current-carrying domains uses a predefined physics interface variable for the Lorentz force distribution in a magnetic flux density B.
Maxwell Stress Tensor
Force and torque calculations using Maxwell’s stress tensor are available in the electrostatics, electric currents, magnetic fields, and magnetic and electric fields interfaces. In electrostatics and electric currents, the force is calculated by integrating
(3-1)
on the surface of the object that the force acts on.
In the Magnetic Fields interface, the expression
is integrated on the surface to obtain the force. In the Magnetic and Electric Fields interface, both expressions are included. E is the electric field, D the electric displacement, H the magnetic field, B the magnetic flux density, and n1 the outward normal from the object. For a theoretical discussion about the stress tensor, see Electromagnetic Forces.
Lorentz Forces
The Lorentz force is defined as F = J × B. The Lorentz force is very accurate for electromagnetic force calculations in electrically conducting domains. The Lorentz force variables are available both in domains and on boundaries (in the case of surface currents).
CYCLE-AVERAGED QUANTITIES
In Frequency Domain studies, the formulas presented above can be used to compute the instantaneous force and torque by taking the real part of all the variables involved. It is often more interesting to compute the average of these quantities over a cycle to, for example, couple the electromagnetic forces to another physics. The cycle-averaged Maxwell’s stress tensor (including both electric and magnetic forces) is computed as: