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

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To calculate the inductance of a solid sphere with electrical contacts, assume a current I flowing through the sphere and determine the magnetic field throughout the sphere. The total magnetic field energy can be found by integrating B^2/(2*μ0) over all space, resulting in a value proportional to I^2. The inductive energy is expressed as L*I^2/2, allowing for the calculation of inductance L by equating the total magnetic field energy to this inductive energy. This method provides a systematic approach to determine the inductance of the sphere. Understanding these calculations is crucial for applications involving electromagnetic fields.
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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