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Magnetic force on a charge outside of toroidal coil

  1. Apr 14, 2015 #1
    1. The problem statement, all variables and given/known data
    Turns of wire would around a toroidal core, carrying a sinusoidal alternating current i(t), represent a toroidal coil in my case. My question is, does magnetic force affect a non-moving charge outside of toroidal core and is there a magnetic field outside of toroidal core? What if the charge moves?

    2. Relevant equations
    Just theoretical explanation.

    3. The attempt at a solution
    I guess there is no magnetic field outside of the core, thus, no force affecting the charge outside of the core, but, I feel like I'm utterly wrong :(
  2. jcsd
  3. Apr 15, 2015 #2


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    Gold Member

    Theoretical explanation: If the coil around the toroidal core is perfect (infinite number of turns) there is no magnetic field outside the core and the coil.

    Practical explanation: There is a magnetic field because the coil is not perfect (finite number of turns). Assume that the number of turns around the core are reduced to zero, having a conductor along the core (but not around), then imagine a circulation path around this conductor (and the core). Now Amperes law states:

    The circulation integral of Hds = N*I.

    Therfore there must be a H-field along this path as N*I = I, ( B = μ0*H ). So as number of turns are reduced, the magnetic field outside the core will become more appearent due to a nonperfect coil. If the number of turns are infinite, no current will pass through this imagined circulation path.
    Last edited: Apr 15, 2015
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