This is an example of the flat (spiral) coil inductance calculation, performed with QuickField simulation software.
Axisymmetric problem of DC magnetics.
All dimensions are in millimeters.
The wire diameter = 1 mm.
The wire material - copper;
The current in the coil I = 1 A.
Determine the inductance of the spiral coil.
We represent the spiral coil in the form of concentric closed circles having the radii of the midlines of each turn. In this formulation, the problem can be modeled as an axisymmetric 2D.
Inductance can be calculated from the energy of the magnetic field W:
L = 2*W/I².
The coil inductance L = 2*9.89*10-8 / 1² = 198 nH.
Magnetic field distribution in the flat concentric coil: