Guidance Requested on Inductance Formula for Solenoid

In summary, the formula for self inductance of a finite solenoid, as given in an EM textbook, is L= (μ(o)* N^2*A * {√(a^2+ l^2) - a} )/l^2 where a=Radius of each turn, l=length of solenoid. The textbook does not provide an explanation for how the formula was derived and only states it as is. The person is requesting guidance from others on how the formula was derived and if it references other sources. It is noted that there may be difficulties in calculating inductance for finite length solenoids and there are other empirical formulas available.
  • #1
warhammer
151
31
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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  • #2
Which textbook is it? Does it point to other textbooks/papers, where the formula is derived?
 
  • #3
I believe that for a finite length solenoid there is a problem with calulating inductance and so there are several emprical formulas available.
 

What is the formula for calculating inductance in a solenoid?

The formula for calculating inductance in a solenoid is L = μN²A/l, where L is the inductance in henries, μ is the permeability of the material, N is the number of turns in the solenoid, A is the cross-sectional area of the solenoid, and l is the length of the solenoid.

How do I determine the number of turns in a solenoid?

The number of turns in a solenoid can be determined by counting the number of times the wire wraps around the core of the solenoid. Alternatively, it can be calculated by dividing the length of the solenoid by the pitch (distance between each turn) of the wire.

What is the unit of measurement for inductance?

Inductance is measured in henries (H), which is equivalent to volts per ampere (V/A).

What factors affect the inductance of a solenoid?

The inductance of a solenoid is affected by the permeability of the material, the number of turns, the cross-sectional area, and the length of the solenoid. It is also affected by the presence of a core material and the frequency of the current passing through the solenoid.

How does the inductance of a solenoid affect its performance?

The inductance of a solenoid is directly proportional to the strength of the magnetic field it produces. This means that a higher inductance will result in a stronger magnetic field and therefore, better performance in applications such as electromagnets and transformers.

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