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Biot-savart law question for an infinite sheet

  1. Apr 4, 2013 #1
    1. The problem statement, all variables and given/known data

    A filamentary conductor carrying current I in the az direction extends along
    the entire negative z axis. At z=0 it connects to a copper sheet that fills the
    x>0,y>0 quadrant of the xy plane. (a) Set up the Biot-Savart law and
    find H everywhere on the z axis; (b) repeat part (a), but with the copper sheet
    occupying the entire x y plane (Hint: express aφ in terms of ax and ay and
    angle φ in the integral).


    2. Relevant equations

    dH=(Idl X ar)/(4pi*r^2)

    3. The attempt at a solution

    Since it wants the H on the z axis im going to ignore the filament since it is on the z axis.

    The current from the filament "I" goes into the sheet so the surface current "K" will be I/(pi/2) since φ ranges from 0 to pi/2 being on the positive xy axis.

    H=∫∫(I/(pi/2)ap X (zaz-pap)/(z^2+p^2)^(1/2))/(4pi*p^2)pdpdφ

    H=I/(2pi^2)∫∫z/(p(z^2+p^2)^(1/2))aφ with φ=0 to pi/2 and p=0 to infinity for the bounds of the integrands

    I did the integral with wolfram alpha and it obviously isnt right. The answer is supposed to be H=I/((2pi^2)z) (ax-ay) A/m for part a and 0 for part b, any help would be greatly appreciated.
     
    Last edited: Apr 4, 2013
  2. jcsd
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