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Inductance of a straight vs toroidal solenoid

  1. Jul 26, 2010 #1

    htg

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    According to widely known formulas, the inductance of a long straight solenoid will remain practically the same if we bend it into a toroidal solenoid. It seems to be a contradiction, because the magnetic path length of a straight solenoid is more than two times greater.
     
  2. jcsd
  3. Jul 28, 2010 #2
    The path length isn't actually important. What matters is the strength of the magnetic field.

    The long solenoid approximation is used because it allows a simplifying assumption that you can ignore any field outside the solenoid as trivially small when you calculate the field inside. (using Stokes theorem and curl B = mu0 J)

    In the case of a toroid, the field actually IS zero outside so the assumption becomes a fact.
    The difference between the two is trivial.
     
  4. Jul 31, 2010 #3

    htg

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    I find it strange (in the light of the Gauss' law) that the flux going through the inside of a long solenoid just comes back on the outside no matter how long the solenoid is.

    In the case of a toroid, I don't think the field on the outside is zero - it is not confined to such a small volume, so its intensity is much smaller.
     
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