self and mutual inductance

[malika]

1) How can I calculate the inductance of a rectangular (superconducting) coil if I know:
- the lenght of each side
- cross section of the rectangular wire(width and thickness)

2)How can I calculate the mutual inductance between two rectangular (superconducting) coils if I know:
- the lenght of each side
- cross section of the rectangular wire(width and thickness)
- their distance

 

[jbartos]

Suggestion to item 1:
Reference:
1. Giacoletto L. J. "Electronics Designers' Handbook," McGraw-Hill Book Co., 2nd Ed, 1977, page 3-45
Self-inductance L of rectangle with Circular Cross Section with the radius rc:
L=(mu/pi)x{a x ln (2a/rc) + b ln (2b/rc) + 2 x (a**2 + b**2)**0.5 - a argsinh(a/b) - b argsinh(b/a) - 2 x (a + b) + [muc x (a + b)/(4 x mu)]}
where
pi is Area/radius**2
mu is permeability of air
muc is permeability of conductor
a is width of rectangular coil
b is length of rectangular coil
Ln is natural logarithm
argsinh is argument of sinh
** sign for exponent
Notice that the circular area = pi x rc**2 = number of turns x area of cross-section of rectangular wire from which rc must be expressed.
For the mutual inductance, the Neumann equation (3.48 on page 3-41) may be used
M21=(mu/4 x pi)(integral over curve 2 integral over curve 1 (cos(beta)/|r|) ds1 x ds2
Beta is the angle between two circuit elements ds1 and ds2