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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.
    Find:
    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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