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Toroidal Solenoid

  1. Nov 26, 2013 #1
    If I have a solenoid in the shape of a toroid (i.e. solenoid joined end to end) the magnetic field produced by the flow of charge will produce a concentrated magnetic field within the coil.

    How would I go about calculating the size of the magnetic field outside of the coil due to magnetic field leakage?

    Any advice much appreciated.

  2. jcsd
  3. Nov 26, 2013 #2


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    I think that a good approximation would be to assume that the magnetic field [itex]\vec{B}[/itex] inside the soldenoid is directed perpendicular to the plane of each coil and is zero outside of the solenoid. Then you can use Ampere's law to compute it:

    [itex]\int B \cdot d\mathcal{l} = \mu I[/itex]

    The meaning of that equation is that if you imagine drawing a closed loop that encloses a bunch of wires, then the total current enclosed by the loop is equal to the line integral of [itex]B[/itex] around the loop.
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