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Homework Help: Magnetic field at the centre of a cable that has an offset hole

  1. Nov 16, 2011 #1
    1. The problem statement, all variables and given/known data
    [From Electromagetism by I. S. Grant & W. R. Phillips, Q4.7]

    A cable of circular cross-section & diameter 0.2 m has a long cylindrical hole with a diameter of 0.001 m drilled in it parallel to the cable axis. The distance between the axis of the hole and cable axis is 0.005 m. The cable has a uniform steady current density of 10[itex]^{5}[/itex]A/m[itex]^{2}[/itex] flowing in it, determine the magnetic field at the centre of the cable.

    Answer: ∏ x 10[itex]^{-6}[/itex] Tesla

    2. Relevant equations

    Ampere's Law

    3. The attempt at a solution

    I know that to find the magnetic field I need to calculate the magnetic field of the cylinder carrying the current density and then add to the field of a current density -J in the opposite direction that would be occupying the hole. I've come up with the equation:

    B = μ/2 * J * (r[itex]_{1}[/itex] - r[itex]_{2}[/itex]) where r[itex]_{1}[/itex] is the distance from the axis of the main cylinder to the centre of it and r[itex]_{2}[/itex] is the distance from the axis of the hole to the centre of the main cylinder. However this gives me an answer of ∏ x 10[itex]^{-4}[/itex] T when I use r[itex]_{1}[/itex] = 0.01 m and r[itex]_{2}[/itex] = 0.005 m.

    What am I doing wrong? Any help is appreciated.
  2. jcsd
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