I'm attempting to solve the Poisson equation in 3D for a magnetic vector potential in the presence of a current source. To validate my code, I'm initially looking to reproduce the model described in the following pair of papers:

The paper gives the following figure to describe the coil which carries the current: enter image description here

Alongside the following parameters:

  • 20 Amps of current.
  • Wire is of type AWG #16 with 861 turns
  • Winding Height (Z axis): 8.89cm
  • Outer Boundary Cross Section: 15.24 cm x 15.24 cm
  • Inner Boundary Cross Section: 10.42 cm x 10.42 cm

I also know that the current density should be homogeneous in a specific element. In this model Jz = 0 throughout and I know J = N*I / A, where A is the cross sectional area, N the number of turns and I the current.


Defining current density in this system can be done by considering the average current density within the winding region, $J_{0}$ (then subdividing this into elements). For winding height h, Inner cross section $L_{1}$, Outer cross section $L_{2}$ with N turns carrying current I:

$ J_{0} = \frac{IN}{h(L_{2} - L_{1})/2} $.

I note this expression does not incorporate the specific wire properties which are also specified in the paper - this maybe to allow physical reconstruction of the system rather than for the modelling side.

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