inductor question

[R.Spinks]

If you have a length (l) of wire coiled to make an inductor and you stretch
the wire (ie. space the coils further) but do not change the diameter (see
www.wowway.com/~rspinks1/question.bmp) is the inductance the same? I
understand inductance to be L = (mu N^2 A) / l + 0.45d. So if I'm stretching
the coils but not changing l
(length) will the inductance change? I guess that technically the cross
sectional area (A) would be changing slightly due to stretching to coils ...
but I'm not sure if that minor variation is negligible - since I'm not
actually changing the diameter. I thought that you compress/decompress
coils (which is what I think this example is) to tune inductance... is this
what's happening? How does a variable inductor work? I have no equipment so
I can't just coil some wire and stretch it myself to see. Insight is
appreciated. Thanks.

 

[John Popelish]

If you have a length (l) of wire coiled to make an inductor and you stretch
the wire (ie. space the coils further) but do not change the diameter (see
www.wowway.com/~rspinks1/question.bmp) is the inductance the same? I
understand inductance to be L = (mu N^2 A) / l + 0.45d. So if I'm stretching
the coils but not changing l
(length) will the inductance change? I guess that technically the cross
sectional area (A) would be changing slightly due to stretching to coils ...
but I'm not sure if that minor variation is negligible - since I'm not
actually changing the diameter. I thought that you compress/decompress
coils (which is what I think this example is) to tune inductance... is this
what's happening? How does a variable inductor work? I have no equipment so
I can't just coil some wire and stretch it myself to see. Insight is
appreciated. Thanks.

Where does your formula come from? The closest reference I could find
was this page:
http://www.qsl.net/in3otd/indcalc.html

A common formula for an air core cylinder coil is Wheeler's formula,

L (microhenries) =(0.8 * N^2 * R^2)/(6*R + 9*L + 10*B).
N = total number of turns
R = average radius = (inner radius + outer radius)/2
L = coil length (along the axis)
B = thickness of the winding = outer radius - inner radius
(all dimensions in inches, coil immersed in air)

The L in that equation does not refer to the length of the wire, but
to the length of the cylinder of the coil's form. So stretching the
coil out into a longer cylinder certainly changes L and thus the
inductance.

 

[R.Spinks]

I got it from "Introduction to Electronics" by Dorf. 2nd Ed. pg. 247 (old
college book)