Force Between Two Concentric Solenoids

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SUMMARY

The discussion centers on calculating the magnetic force between two concentric solenoids, where the outer solenoid has a time-varying current and the inner solenoid is coaxial and free to slide. The outer solenoid has an outer radius R1 and an inner radius R2, while the inner solenoid has an outer radius equal to R2. The primary inquiry is whether the magnetic force on the inner solenoid can be calculated analytically or if numerical methods are required. The problem can be simplified by considering both solenoids as thin shells, focusing on the interaction between them.

PREREQUISITES
  • Understanding of electromagnetic theory, specifically Ampère's Law and Faraday's Law of Induction.
  • Familiarity with the concept of induced current in conductive loops.
  • Knowledge of solenoid geometry and magnetic field calculations.
  • Basic skills in numerical methods for solving electromagnetic problems.
NEXT STEPS
  • Research the application of Ampère's Law to calculate magnetic fields in solenoids.
  • Explore Faraday's Law of Induction to understand induced currents in the inner solenoid.
  • Investigate numerical methods for solving electromagnetic field problems, such as finite element analysis.
  • Study the effects of solenoid geometry on magnetic interactions, particularly in coaxial configurations.
USEFUL FOR

Physicists, electrical engineers, and students studying electromagnetism, particularly those interested in solenoid interactions and induced currents.

dgreenheck
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Imagine a finite length solenoid with outer radius R1 and inner radius R2. This solenoid has a time-varying current going though it. This solenoid is also fixed so that it cannot move. Now imagine another solenoid, coaxial with the first, with its outer radius equal to R2 such that it can slide in and out of the first solenoid. The ends of this solenoid are connected together and no current is being externally applied to it. The only current going through it is the induced current from the first coil. My question is, would it be possible to calculate the magnetic force on this solenoid? Or is this a problem that would need to be solved numerically?
 
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My question can be simplified so that both solenoids are a thin shell instead of having a finite thickness. I'm just wondering how one solenoid within another reacts.
 

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