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Torque on a Current Loop

  1. Mar 11, 2012 #1
    1. The problem statement, all variables and given/known data
    An electron moves in a circle of radius r = 5.29 x 10^-11 m with speed 2.19 x 10^6 m/s. Treat the circular path as a current loop with a constant current equal to the ratio of the electron's charge magnitude to the period of the motion. If the circle lies in a uniform magnetic field of magnitude B = 7.10 mT, what is the maximum possible magnitude of the torque produced on the loop by the field?

    2. Relevant equations

    3. The attempt at a solution

    Here's my attempt, could you tell me if it is the correct approach?
    Ok, so we can use τ(tao) = μB (sinθ). Since we are trying to figure out the maximum torque, then it must appear at 90 degrees since (sin 90) = 1.
    So now we replace μ with μ=NiA, where i is current, A is area, and N is the number of coils. Here, N is 1 since there is only 1 loop.
    Now we need to determine current. As the question states, current is the ratio of electron charge and period of motion. Period is T = circumference/speed. T = 2∏r/2.19 x 10^6 = 1.5177 s. Then i = q/T, so i = 1.602 x 10-19 / 1.5177 = 0.001055531 A.
    Sub "i" back into τ=iAB = (0.001055531)(∏)(5.29 x 10 ^-11)(5.29 x 10^-11)(7.1 x 10 ^-3) = 6.59 x 10^-26 N*m
    Last edited: Mar 11, 2012
  2. jcsd
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