Guidance Requested on Inductance Formula for Solenoid

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SUMMARY

The self-inductance formula for a finite solenoid is given by L = (μ(o) * N^2 * A * {√(a^2 + l^2) - a}) / l^2, where 'a' is the radius of each turn and 'l' is the length of the solenoid. The discussion highlights the lack of derivation details in the referenced textbook, prompting members to seek guidance on the geometric principles involved. Additionally, the conversation points out the existence of empirical formulas for calculating inductance in finite-length solenoids, indicating a need for further exploration of these alternatives.

PREREQUISITES
  • Understanding of electromagnetic theory and self-inductance
  • Familiarity with solenoid geometry and parameters (radius, length)
  • Knowledge of magnetic permeability (μ(o)) and its significance
  • Basic mathematical skills for manipulating algebraic formulas
NEXT STEPS
  • Research the derivation of the self-inductance formula for finite solenoids
  • Explore empirical formulas for calculating inductance in finite-length solenoids
  • Study relevant sections in textbooks on electromagnetic theory, such as "Introduction to Electrodynamics" by David J. Griffiths
  • Investigate online resources or academic papers that discuss solenoid inductance calculations
USEFUL FOR

Students and professionals in electrical engineering, physicists studying electromagnetism, and anyone involved in designing or analyzing solenoid applications.

warhammer
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In my textbook on EM, the formula for self inductance of a finite solenoid is given as:

L= (μ(o)* N^2*A * {√(a^2+ l^2) - a} )/l^2 where a=Radius of each turn, l=length of solenoid.

I am having trouble and extreme difficulty in trying to ascertain how this formula was derived in the book and what kind of geometry. They have not provided any explanations and simply stated the same.

I request guidance/hint from PF Members as to how this formula was derived.
 
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Which textbook is it? Does it point to other textbooks/papers, where the formula is derived?
 
I believe that for a finite length solenoid there is a problem with calulating inductance and so there are several emprical formulas available.
 

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