Need a Review of Solenoid Equations and their Derivation

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SUMMARY

This discussion focuses on the derivation and understanding of solenoid equations, specifically for bar solenoids and toroidal solenoids, including those with air gaps. The inductance of a bar-shaped air-core solenoid is defined by the equation L = μ0AN²/l, where A is the cross-sectional area, N is the number of turns, and l is the length of the solenoid. For toroidal solenoids, the same inductance formula applies, substituting the circumference of the torus for l, provided the major radius significantly exceeds the minor radius. The discussion highlights the complexities introduced when a magnetic core is inserted into the solenoid.

PREREQUISITES
  • Understanding of Maxwell's equations in integral form
  • Familiarity with solenoid geometry and dimensions
  • Knowledge of magnetic permeability (μ0)
  • Basic principles of electromagnetism and inductance
NEXT STEPS
  • Study the derivation of solenoid equations using Maxwell's equations
  • Explore the effects of magnetic cores on solenoid inductance
  • Learn about the differences in inductance calculations for various solenoid configurations
  • Investigate practical applications of toroidal solenoids in electrical engineering
USEFUL FOR

Students and professionals in physics and electrical engineering, particularly those focusing on electromagnetism, solenoid design, and inductance calculations.

Prince Rilian
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I need a review of solenoid equations, such as equations for bar solenoids, toroidal solenoids, and toroidal solenoids with an air gap within them. I think that somewhere along the line I may have learned something incorrect, so I would like to kill any douts that I have by ascertaining myself of the correct equations.
 
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the bar (straight) solenoid is the simplest. You can derive the magnetic field by using Maxwell's equations (in integral form). For the toroidal solenoid, I guess it is more complicated, unless the major radius is much greater than the minor radius, in which case I guess it would be approximately the same as in the case of the straight solenoid.
 
I know that the equation for the inductance of a bar-shaped air-core solenoid is

L = μ0AN2/l,​

assuming that both of the dimensions of the area component are much less than the variable "l". For a toroidal solenoid, I know that you can use the same form of equation if you use the circumference of the torus in place of "l".

The problem in my understanding seems to come about once a magnetic core is inserted into the solenoid...
 

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