Energy stored in a toroid

  1. Calculate the energy stored in a toroidal coil.

    The magnetic field in a toroid is give by: [itex]B = \frac{\mu_0 n I}{2\pi r}[/itex]

    Energy stored is given by:
    [tex]W = {1\over 2\mu_0}\int B^2 d\tau[/tex]

    [tex]W = {1\over 2\mu_0} \frac{\mu_0^2 n^2 I^2}{4\pi^2}\int {1\over r^2}d\tau[/tex]

    How do I determine the volume element for a toroid?
     
  2. jcsd
  3. Meir Achuz

    Meir Achuz 2,061
    Science Advisor
    Homework Helper
    Gold Member

    The toroid can usually be approximated by a solenoid of length 2\pi R,
    with r constant inside the toroid. Then V=(2\pi L)*(\pi a^2), with B constant.
     
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