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Solenoids and Toroids

  1. Jun 28, 2008 #1
    Hi everyone.
    I need help please.
    I am working on problems with solenoids and Toroids
    I have solution for the solenoid:
    B = μo i n

    And toroid:
    B = (μ o i n)/ (2Π r)
    Also, I know that the magnetic field is the function of r namely: B = B(r)

    r- radius of the Ampere’s path
    n – number of loops per unit length
    μo – constant

    My problem is:
    Using the solution for the toroid, show that for the large toroid the answer can be approximated as the solenoid on the very small piece of the toroid.
    I know that I have to play with limits. Something like:
    a - inner radius of the toroid,
    b – outer radius of the toroid,
    ∆a - the difference between radius a and radius b.
    I think I have to take a limit when ∆a goes to 0 and in this way radius a will approach radius b. in this way the solution for the toroid SHOULD be the solution for the solenoid (on the small length L of course)
    I don’t know how to set it up. How to get from the toroid solution to the solenoid solution using limits or (other technique)

    Thanks for help
    Chris W
  2. jcsd
  3. Jun 28, 2008 #2
    Can anyone please help me here... thanks
    Chris W
  4. Jun 29, 2008 #3


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    Homework Helper

    Hi Chris W,

    Your toroid magnetic field equation is not quite right. It should be:

    B = \frac{\mu_0 i N }{2\pi r}

    where N is the total number of turns (not turns per length). Notice that [itex]N/(2 \pi r)[/itex] is in a way similar to the n in the solenoid formula; but what is the difference? If you then think about your limiting process that should help you get the result.
  5. Jun 29, 2008 #4
  6. Jun 29, 2008 #5
    Thanks Guys. I love this forum
    Chris W
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