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Zero B Field Inside within Hollow Wire

  1. Aug 6, 2016 #1
    1. The problem statement, all variables and given/known data
    A long, thin wire carrying constant current I1 = 2 A into the page is surrounded by a concentric cylindrical hollow wire of inner radius a = 0.12 m, and outer radius b= 0.26 m, carrying total current I2 = 4 A directed out of the page, as shown. Assume the current in the cylindrical hollow wire is distributed uniformly over its cross-sectional area.

    fig17.gif

    At what radius is B = 0 in the region a < r < b inside the hollow wire?

    (A) .19 m
    (B) .20 m
    (C) .21 m
    (D) .25 m
    (E) The magnetic field is not zero anywhere inside the hollow wire.

    2. Relevant equations
    Ampere's Law

    3. The attempt at a solution
    Using ratios:
    ##I_r → 2π(r-a)##
    ##I_b → 2π(b-a)##
    ##I_{enc} = I_2 \frac{I_r}{I_b} - I_1 = (4A) \frac{r-a}{b-a} - I_1##
    ##b-a = .14##
    ##\frac{r-.12}{.14} = 1/2##
    ##r = .19 m##

    The answer however is not A. What am I doing wrong?
     
  2. jcsd
  3. Aug 6, 2016 #2
    $$|\mathbf{B}| = \frac{\mu_0 I_{enc}}{2\pi r} $$

    I am not sure you are correctly expressing ##I_{enc}## as a function of ##r##. It is going to be related to the area of an annulus. So I would expect to see ##r^2## somewhere in your work.
     
  4. Aug 7, 2016 #3

    rude man

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    Apply Ampere's law anywhere in the region a < r < b. What do you get?
     
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