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Helmholtz coil proof

  • 03-01-2007 12:10pm
    #1
    fluppet
    Closed Accounts Posts: 232 ✭✭


    I have to prove that the magnetic field in a Helmholtz coil set-up is the most uniform when the distance between the coils is equal to the radius of the coils. It sounded to me like the kind of thing I could find on the internet, but I have been unsuccessful. Does anyone have any ideas?

    The most obvious thing (although not the most elegant) thing seemed to be to write an expression for the magnetic field at the centre (x=d/2, where d is the distance between the coils) and then another for the field at one side (x=0). Then get the difference between them and differentiate wrt d to work out the value of d that gives the minimum. Unfortunately I don't seem to be getting exactly the right answer.

    I don't think I made any mistakes, but what I get at the end of it is:

    (d^2)/(4) - 2^(2/5).d^2 = 2^(2/5).r^2 - r^2

    Which as you can see is quite close. I can probably disregard the difference in sign (most likely a sign-error somewhere), but it's that division of the first d^2 by 4 that's the problem - if that wasn't there then I could say d=r.

    Does anyone have any better ideas (no messy Bessel functions, etc. please), or suggestions for why my approach didn't work?

    Thanks


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