1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook