How do you calculate the inductance of a metal sphere with electrical contacts?

[John Shillington]

Hey everyone this is my first thread i was wondering how you calculate the inductance of a solid sphere. Say a sphere for example of 5cm diameter with electrical contacts on opposing sides 0.5 cm in diameter.
Any help would be much appreciated

 

[phyzguy]

The simplest way is to assume a current I flowing through the sphere. Then, given this I, calculate the magnetic field everywhere. Then, calculate the total magnetic field energy by integrating B^2/(2*μ0) over all space. This should give an answer proportional to I^2. The total inductive energy is L*I^2/2, so you can calculate L by equating the total magnetic field energy to the inductive energy L I^2/2.

 

[John Shillington]

Thanks for your reply, it was informative.