The Hall effect is available using the electromagnetic analysis option (KEYOPT(1) = 1) of the 3D electromagnetic elements SOLID236 and SOLID237.

The Hall effect analysis is nonlinear and requires at least two iterations to achieve a converged solution. The Newton-Raphson algorithm will be turned on automatically when the Hall constant is specified. An electromagnetic analysis with the Hall effect can be steady-state or transient.

The electric constitutive relation is generalized as follows to include the Hall effect:

(5–189)

where:

{J} = electric current density vector

= electric conductivity matrix without a magnetic field

ρ _xx = electrical resistivity in the X-direction (input as RSVX on MP command)

{E} = electric field intensity vector

{E _H } = –R _H [{J} x {B}] = Hall field intensity vector

R _H = Hall coefficient (input as RH on MP command)

{B}={B _x, B _y , B _z }^T = magnetic flux density vector

Combining ohmic and Hall conductivity terms, Equation 5–189 can be rewritten using an effective anisotropic and nonsymmetric conductivity:

(5–190)

where:

(5–191)