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Homework Help: Ampere's Law

  1. Jun 6, 2007 #1
    1. The problem statement, all variables and given/known data

    What is the magnitude of the magnetic field at point P if a=R and b=2R (see attached image)

    2. Relevant equations
    Ampere's Law where integral of B ds over a closed surface = μ0I where μ0= 4πx10-7

    3. The attempt at a solution

    I used the formula and found after integrating (ds becomes 2*Pi*2R the circumference of the circle) that for the outer circle (radius 2R) B= μ0I/4*Pi*R

    I then thought that the current through the inner circle would be in the same ratio as that of the areas of the two circles.
    So inner current/outer current = Pi*(2R)^2/Pi*R^2
    so inner current = 4I

    i then subsituted this into my integral for the inner circle using Ampere's Law and found B for the inner circle to be equal to μ0*4I/2*Pi*R which simplifies to μ0*2I/Pi*R

    the next step is what i'm having problems with as i'm not 100% certain as to what to do with these two values of B i have found. current flows in the same direction in both so i thought id have to add one B to the other but none of these answers show up in the five multiple choice options so i must have gone wrong somewhere. have i perhaps missed a crucial step along the way or was my working out in the first place off the mark? any advice would be great

    cheers :smile:

    Attached Files:

  2. jcsd
  3. Jun 6, 2007 #2

    Doc Al

    User Avatar

    Staff: Mentor

    I can't quite follow the path that you are integrating over. Rather that attempt to use Ampere's law, why not use the Biot_Savart law to calculate the magnetic field at the center of a current loop. Unless you happen to the know the formula already.
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