Calculating Inductance of a Solenoid with Multiple Isolated Loops

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To calculate the inductance of a solenoid composed of N isolated loops, each connected to its own battery, one can start by determining the inductance for each individual loop. The total inductance can then be found by summing the inductance contributions from each loop. This approach considers the geometry and number of loops, ensuring that the unique characteristics of each loop are accounted for. The formula for inductance can be applied to each loop separately before aggregation. This method provides a comprehensive way to assess the inductance of a solenoid with multiple isolated loops.
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I found this formula to approximate the inductance of a coil of wire. But what if a solenoid were composed of N separate loops, where each loop of the solenoid is connected to its own battery? That is, what if the solenoid had the same number of loops and the same geometry, except that each loop is isolated from the others and has its own separate power supply. How would you calculate the inductance of such a solenoid? (See attached Snapshot.jpg)
 

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You could calculate the induction due to each loop and add them up to find the total induction.
 
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