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Calculating magnetic field of finite solenoid

  1. May 20, 2012 #1
    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
    Inner Radius = 0.008m
    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?
  2. jcsd
  3. May 20, 2012 #2


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    welcome to pf!

    hey bsully! welcome to pf! :smile:
    no, the turns per length (the pitch) is N/L, which is constant :smile:

    (btw, i couldn't see anything at http://www.image-share.com/ijpg-1492-27.htm [Broken] :redface:)
    Last edited by a moderator: May 6, 2017
  4. May 20, 2012 #3
    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.
  5. May 20, 2012 #4
    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)
    Last edited by a moderator: May 6, 2017
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