Homework Help: Inductance of solenoid (length = diameter)

1. Mar 3, 2016

lcr2139

1. The problem statement, all variables and given/known data
a solenoid inductor consists of 200 closely spaced turns, length = diameter = 5cm. calculate inductance.

2. Relevant equations

3. The attempt at a solution
H = NI/L
L = N (flux) / I - you cant use this because the length is equal to the diameter. What equation do I use?

2. Mar 3, 2016

The magnetic flux needs to be included as a function of position to get the total flux and thereby the total inductance. The simplest solution for the B field for a finite length solenoid (it turns out to be exact), is to use a result from the "pole method" of magnetostatics. The B (M.K.S. units) inside the solenoid will be equal to $B_z= n*\mu_o*I$ plus a subtractive correction term of the B from poles of surface magnetic charge density $\sigma_m=n*\mu_o*I$ with a "+" pole on the right and a "-" pole on the left. The magnetic surface charge density in this mathematical solution is considered to be uniform over the opening of the solenoid. I don't have a "link" for you, but I do think you could possibly find this solution in one of the older and more advanced E&M texts. One result you get from the above is that the B field at the openings of any finite length solenoid is exactly half of the value that it takes on for one of infinite length.

3. Mar 3, 2016

Hesch

If you google inductance+solenoid+calculator you will find different equations, and by using different calculators, you will get different results because the equations they are using are approximations.

The most popular approximation is:

L = μ0 * N2 * A / L(ength) , A = cross section area.

I think a more precise result is found, calculating the B-field ( at 1 A ) at different locations inside the solenoid, then integrating the B-fields to a flux passing through every turn.

Use Biot-Savart.

Having your program up and running, the calculation can be done within say 20 minutes.