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

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SUMMARY

The inductance of a solid sphere can be calculated by assuming a current I flowing through the sphere and determining the magnetic field generated. For a sphere with a diameter of 5 cm and electrical contacts of 0.5 cm on opposing sides, the total magnetic field energy can be computed by integrating B^2/(2*μ0) over all space. This energy is proportional to I^2, allowing for the calculation of inductance L by equating the total magnetic field energy to the inductive energy L I^2/2.

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John Shillington
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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
 
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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.
 
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Thanks for your reply, it was informative.
 
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