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Magnetostatics - magnetic flux and energy in toroidal inductor

  1. Apr 27, 2009 #1
    1. The problem statement, all variables and given/known data
    A toroidal inductor consists of 500 turns of wire on a ring-shaped core of magnetic material with a relative permeability of 8000. The core has a square cross-section with an internal radius of 20mm, external radius of 40mm and height of 20mm.
    a) Magnetic flux in the core
    b) Magnetic energy stored in the inductor
    when the current in the winding is 50mA

    2. Relevant equations
    Magnetic flux = [tex]\int\int[/tex]B.dS
    (1) B = [tex]\mu[/tex]0[tex]\mu[/tex]r H
    (2) H = (NI)/(2[tex]\pi[/tex]R)
    Ampere's Law: [tex]\int[/tex]B.dL = [tex]\mu[/tex]0 I

    Energy Um = (1/2)I[tex]\Phi[/tex]

    3. The attempt at a solution
    a) From (1) and (2), B = [tex]\mu[/tex]0[tex]\mu[/tex]r (NI)/(2[tex]\pi[/tex]R)
    where R is the radius from the centre of the torus to the centre of the core.
    Magnetic flux = [tex]\Phi[/tex] = B [tex]\int\int[/tex]dS = [tex]\mu[/tex]0[tex]\mu[/tex]r (NI)/(2[tex]\pi[/tex]R) (2[tex]\pi[/tex]R)(4h)
    = [tex]\mu[/tex]0[tex]\mu[/tex]rNI(4h)
    Plugging in [tex]\mu[/tex]r = 8000, I = 50 x 10-3, N = 500, h = 20 x 10-3 gives [tex]\Phi[/tex]=0.0201Wb

    Is this right? If not, where did I go wrong, how do I fix it?

    b) Um = (1/2)(50 x 10-3)(0.0201) = 5.03 x 10-4 J

    Again, is this right? I'm not comfortable with this course at all. If it's incorrect, how do I fix it? What do I do?

    Thanks in advance.
    Last edited: Apr 27, 2009
  2. jcsd
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