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Infinitely long cylinder - locate bound currents and calculate field

  1. Nov 14, 2011 #1
    1. The problem statement, all variables and given/known data

    An infinitely long cylinder, of radius R, carries a frozen-in magnetisation, parallel to the z-axis, M=ks k-hat, where k is a constant and s is the distance from the axis. There is no free current anywhere. Find the magnetic field B inside and outside the cylinder by two different methods:

    i) Locate all bound currents, and calculate the field they produce; and
    ii) Use Ampere's law, the loop integral of H.dl=I(subscript enc), to find H, then get Bfrom H=(1/mu0)B-M

    3. The attempt at a solution
    I found the answer on http://www.nhn.ou.edu/~shaferry/41832005_files/finalsol.pdf

    but what I don't understand is why far away from the loop the B field must go to zero. I would be grateful if someone could explain please.
     
  2. jcsd
  3. Nov 14, 2011 #2

    rude man

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    but what I don't understand is why far away from the loop the B field must go to zero. I would be grateful if someone could explain please.[/QUOTE]

    Same reason that B outside an infinitely long solenoid is zero. Looking at a given section of the solenoid, coil currents flow in opposite directions along the two sides of the solenoid, canceling the external field. A permanent-magnet cylinder is no different if magnetization is along the major axis (center). Amperian currents merely assume the role played by a solenoid's current-carrying wire.

    So B doesn't just disappear at infinity, it disappears anywhere outside the OD of the rod.

    This can be proven more rigorously by application of the Biot-Savart law.

    cf. Resnick & Halliday, sect. 34-5.
     
  4. Nov 15, 2011 #3
    the current loop need to enclose some sort of current for there to be any sort of magnetic field this is why outside a solenoid the B field is zero
     
  5. Nov 15, 2011 #4

    rude man

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    That only means that the circulation (closed-path integral) of B is zero. It does not preclude segments of the path being finite, as long as they cancel around the path.

    Example: a single loop of curent-carrying wire. Choose a closed path in front of the loop but not intersected by the loop. B is certainly not zero in front of the loop!
     
  6. Nov 15, 2011 #5
    thanks,
    for que i), why is the field due to the volume distribution=mu0 k(R-s)z-hat?
    The bound current due to the volume is curl M=- k phi-hat, but how does this lead to:

    the field due to the volume distribution=mu0 k(R-s)z-hat?
     
  7. Nov 16, 2011 #6

    rude man

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    I'm sorry no one's replied to that, incl. me. Truth is, I don't know the answer without researching the subject more myself.
     
  8. Nov 17, 2011 #7
    thanks anyway. think i found out in the end, though
     
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