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Magnetic flux outside cylindrical conductor

  1. Jan 25, 2006 #1
    Hey everyone,

    I have failed to show that the magnetic flux outside a cylindrical conductor is zero.

    The problem goes like this:

    a coaxial cable consists of a solid inner cylindrical conductor of radius a and an outer cylindrical conductor of inner and outer radius b and c. Distributed currents of equal magnitude I flow in opposite directions in the two conductors. Derive expressions for the magnetic flux density B(r) for each of these regions

    1) 0<r <a

    by amperes law I showed: [tex] B = \frac {K *l*r} {2*pi*a^2} [/tex]

    where K is the permeability of free space, don't know how to write that with latex

    2) a<r<b

    again by amperes law: [tex] B = \frac {K *l} {2*pi*r} [/tex]

    3) b<r<c

    again by amperes law: [tex] B = \frac {K *l*(r^2-b^2)} {2*pi*r*(c^2-b^2)} [/tex]

    4) c<r

    I got stuck here, surely it must be zero....but how can that be shown?

    thanks for your help - it's very much appreciated
  2. jcsd
  3. Jan 25, 2006 #2


    User Avatar

    Staff: Mentor

    With the coaxial cable coming out of the paper at you, draw a circular closed path around the outside of it.

    INTEG[B dot dL] around that closed path = mu * I(enclosed)

    The total I enclosed by the circle is zero, since the current up the inner conductor is the same as the current down the outer conductor, so B (or H) has to be identically zero everywhere outside the coax.

    Edit -- BTW, check your answer for (3). When r=c, you should get zero for H.
    Last edited: Jan 25, 2006
  4. Jan 26, 2006 #3
    Thanks Berkeman - that's explained it and it's very much appreciated!! :-) As for the third one it surely has to be (c^2-r^2)/(c^2-b^2)
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