# Calculating magnetic field of finite solenoid

Hey guys! New guy here so bear with me on my first post:)

I'm trying to calculate the B field in the center of a finite solenoid for different outer radius sizes. I was able to find a formula online that gave the B field in the center of a solenoid given its length, inner radius, outer radius, number of loops, and current.

(sorry guys but I cant include links until I reach 10 posts - add "www" to each link)
Formula: .netdenizen.com/emagnet/solenoids/solenoidonaxis.htm

Using matlab, I plotted a graph of the B field with the outer radius as the input variable and all other variables constant. Here's the graph I created:

L = 0.0254m
I = 100A
N = 100
Outer Radius varies from 0.008m to 1 m

IMAGE: .image-share.com/ijpg-1492-27.htm

Shouldn't the B field increase with increasing outer radius due to there being more turns per unit length?

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tiny-tim
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welcome to pf!

hey bsully! welcome to pf!
L = 0.0254m
I = 100A
N = 100
Outer Radius varies from 0.008m to 1 m

Shouldn't the B field increase with increasing outer radius due to there being more turns per unit length?
no, the turns per length (the pitch) is N/L, which is constant

(btw, i couldn't see anything at http://www.image-share.com/ijpg-1492-27.htm [Broken] )

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Well now I'm embarrassed... I blame it on my lack of sleep:)

So based on what I have so far, I've found the B field for a solenoid with increasing outer radius but with a constant number of turns - i.e. the wire diameter is increased to maintain dimension.

I guess what I was trying to do was to keep the wire diameter constant - thus number of turns won't be constant. For example, find the B field inside a solenoid as I add layers of the same diameter wire(solenoid length, inner radius, and current kept constant). I figured this would be a way to decide at what point adding another layer of wiring to a solenoid would be useless as it wouldn't contribute much to the central B field.

finally figured it out.. replace N(number of turns) in the formula with N = (L/Dia)*((RO-RI)/Dia) where L = length of solenoid, RO = outer radius, RI = inner radius, and Dia = the diameter of the wire you are using.

Plugging into the formula:
L = 0.0254m (1 inch)
RI = 0.005m (5mm)
Dia = 0.001m (1mm)
I = 30Amps

0.005m < RO < 0.05m

i49.tinypic.com/1fxyzc.jpg (add 'http://' [Broken] at the beginning - hope this works)

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