I Guidance Requested on Inductance Formula for Solenoid

AI Thread Summary
The formula for the self-inductance of a finite solenoid is presented as 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 user is struggling to understand the derivation of this formula and is seeking guidance on the geometric considerations involved. They also inquire about the textbook source and whether there are other references that explain the derivation. Additionally, the discussion highlights that calculating inductance for finite-length solenoids can be complex, with various empirical formulas available. Clarification on these points would greatly assist in understanding the topic.
warhammer
Messages
164
Reaction score
33
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.
 
Physics news on Phys.org
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.
 
This is from Griffiths' Electrodynamics, 3rd edition, page 352. I am trying to calculate the divergence of the Maxwell stress tensor. The tensor is given as ##T_{ij} =\epsilon_0 (E_iE_j-\frac 1 2 \delta_{ij} E^2)+\frac 1 {\mu_0}(B_iB_j-\frac 1 2 \delta_{ij} B^2)##. To make things easier, I just want to focus on the part with the electrical field, i.e. I want to find the divergence of ##E_{ij}=E_iE_j-\frac 1 2 \delta_{ij}E^2##. In matrix form, this tensor should look like this...
Thread 'Applying the Gauss (1835) formula for force between 2 parallel DC currents'
Please can anyone either:- (1) point me to a derivation of the perpendicular force (Fy) between two very long parallel wires carrying steady currents utilising the formula of Gauss for the force F along the line r between 2 charges? Or alternatively (2) point out where I have gone wrong in my method? I am having problems with calculating the direction and magnitude of the force as expected from modern (Biot-Savart-Maxwell-Lorentz) formula. Here is my method and results so far:- This...
Back
Top