1. Not finding help here? Sign up for a free 30min 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!

Amperes law: magnetic field inside an infinite slab containing a volume current.

  1. Jan 30, 2012 #1
    1. The problem statement, all variables and given/known data
    an infinite slab is centered on the xy plane. the top of the slap is at z=a/2, the bottom of the slab is at z= -a/2. A volume current (J) is set up within the slab. find B everywhere

    J = k (1 - z^2/a^2) [itex]\hat{y}[/itex]
    2. Relevant equations

    amperes law

    3. The attempt at a solution

    the only thing I am confused about is finding B inside the slab.

    I was going to set up my amperian loop as a rectangle, which is oriented perpendicular to the volume current.

    The rectangle would extend a distance z above and below z=0 (z still inside the slab)

    however my text book mentions B is discontinious at a surface current, so i am uncertain if my amperian loop takes that into account.

    But given the stuff we have learned so far, I am very confident that we are supposed to apply amperes law to this situation.

    Can anyone explain if you can still apply amperes law for points inside a volume current?
     
  2. jcsd
  3. Jan 31, 2012 #2

    rude man

    User Avatar
    Homework Helper
    Gold Member

    The only way i see is to
    (1) detrmine the vector potential A = (1/4π)∫idv/r
    where i = current density across a surface in elemental volume dv anywhere within the slab,
    and r = distance from dv to the point of observation. Since i has a y component only, so will A. So A = Ay y.

    dv = dx*dy*dz and extends from -∞ < x < ∞, -∞ < y < ∞, and -a/2 < z < a/2
    for the part inside the slab. For the outside, integration is limited to |z| > a/2.
    r is the distance from each dv to (x,y,z).

    This looks like a horrible pair of volume integrals to me!

    (2) If you did solve for Ay you could then find B from
    B = μ*curl (Ay y).

    Sorry this is the best I could do.
     
  4. Jan 31, 2012 #3
    so I think I may have left out the most important piece of information to this problem:

    the slab is made of a diamagnetic material (linear media, magnetization antiparallel to B)

    then inside the slab, you apply amperes law for the auxilary field H

    B=μ[itex]_{o}[/itex](1+χ[itex]_{m}[/itex])H

    where the magnetization M =χ[itex]_{m}[/itex]H

    So this discontinuity I was so worried about is due to the magnetization?
    (M should produce a surface current, which is exactly the source of B's discontinuity)


    I am pretty comfortable doing these types of problems mathematically, but is my reasoning sound?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Amperes law: magnetic field inside an infinite slab containing a volume current.
Loading...