Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Show that for a ferromagnetic material the field in the gap is given by?

  1. Nov 10, 2011 #1
    1. The problem statement, all variables and given/known data

    A toroidal shaped magnetic material of radius, a, and cross sectional radius R has a small transverse gap cut into it of length l. The toroid is uniformly overwound with a coil of N loops carrying a current I. Show that for a ferromagnetic material the field in the gap is given by

    B~mu0 N I/l

    [5 marks]

    3. The attempt at a solution

    Assume that the curvature is small, so that locally B, H and M are parallel to each other, uniform across the cross-section and tangential. A circular loop integral of radius R will have the same value of H at every point, so:

    the loop integral of H.dl=H 2 pi R=NI

    H=NI/2 piR

    2 pi R is the circumference, so for a toroid with a gap of length l:

    H=NI/l

    B=mu0(H+M)

    M=0 because the gap is made of empty space

    B=mu0 (H+0)

    =mu0 NI/l

    Have I gone wrong somewhere by saying something that's not true? I'd be grateful if you could help please.
     
  2. jcsd
  3. Nov 11, 2011 #2

    rude man

    User Avatar
    Homework Helper
    Gold Member

    If H = Ni/2piR, then it's kind of hard to believe that H = Ni/l, isn't it?

    Hint: what is Ni, which is magnetomotive force, in terms of H(gap), H(material), l and R?
     
  4. Nov 11, 2011 #3
    NI is the magneetic force? The number of turns on the toroid multiplied by the current is the magnetic force?
     
  5. Nov 11, 2011 #4

    rude man

    User Avatar
    Homework Helper
    Gold Member

    I know it by "magnetomotive" force, mmf. It's the magnetic equivalent of electromotive force in electricity.

    In electricity, it's emf = -N*∂φ/∂t = iR = El, i = current, R = resistance, φ = magnetic flux, N = no. of turns, R = l/σA, A = area, σ = conductivity, l = path length, E = electric field.

    In magnetics, it's mmf = Ni = φR' = Hl, R' = magnetic reluctance, H = magnetic intensity, R' = l/μA, μ = permeability, B = μH.
     
    Last edited: Nov 11, 2011
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook