Edge Force Density

The edge density is available only in Maxwell 2D. It is available only on object outlines adjacent to air or vacuum space. It is defined as

where B and E are the magnetic flux density and electric field intensity at the midpoint of the edge, respectively, and n is the outward normal direction of the edge. µ and e are the permeability and permittivity in the ith neighboring element. For the electrostatic, AC, and DC solvers, only the electric field is included; while for the magnetostatic, eddy current, and magnetic transient solvers, only the magnetic field is considered. For the AC and eddy current solvers, edge force density is the averaged (DC) force density.

Surface Force Density

In Maxwell 2D, surface force density is defined as

where N is the number of sides of the element, l_i is the length of side i of the element. For the RZ case, r_i and r_c are the radius of side i and the radius of the element center, respectively. µ and e are the permeability and permittivity in the ith neighboring element. In the XY plane, r_i and r_c are set to 1.

In Maxwell 3D, surface force density is only available on object faces adjacent to air or vacuum space. It is defined as

where B and E are the magnetic flux density and electric field intensity at the center of the surface face, respectively, and n is the outward normal direction of the surface face. For the electrostatic, AC, and DC solvers, only the electric field is included; while for the magnetostatic, eddy current, and magnetic transient solvers, only the magnetic field is considered. For the AC and eddy current solvers, surface force density is the averaged (DC) force density.

Volume Force Density

Volume force density is only available in Maxwell 3D. It is calculated as

µ and e are the permeability and permittivity in the ith neighboring element. A_i is area of side i of element. For the electrostatic, AC, and DC solvers, only the electric field is included; while for the magnetostatic, eddy current, and magnetic transient solvers, only the magnetic field is considered. For the AC and eddy current solvers, volume force density is the averaged (DC) force density.

Lorentz force density is calculated instead of volume force density in pure conductors containing source current in magnetostatic, eddy current, and magnetic transient solvers: f = J x B