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13 January, 17:04

Two concentric current loops lie in the same plane. The smaller loop has a radius of 2.7cm and a current of 12 A. The bigger loop has a current of 20 A. The magnetic field at the center of the loops is found to be zero. What is the radius of the bigger loop?

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  1. 13 January, 17:18
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    The B-field at the center of a circular loop of radius, r and current, I is;

    Magnetic field, B = (μ * I) : 2pi * R

    Given:

    rs = 2.7 cm

    = 0.027 m

    Is = 12 A

    Ib = 20 A

    (μ * Is) / 2 * rs = (μ * Ib) / 2 * rb

    Inputting values,

    rb = (20 * 2 * 0.027) / 12 * 2

    = 0.045 m

    = 4.5 cm.
  2. 13 January, 17:19
    0
    Radius of bigger loop (R) = 4.5cm

    Explanation:

    Consider a circular path of radius r around the wire. The magnetic field along that path is given by;

    ∫B*dl = k*I where I is the current enclosed. From symmetry, ∫B*dl = 2*π*r*B

    B = K*I/r, so the magnetic field varies inversely as the loop radius and directly as the current.

    The smaller loop current to radius ratio is 12/2.7

    The bigger loop current to radius ratio is = 20/R

    12/2.7 = 20/R

    R = (20 * 2.7) / 12

    R=54/12

    R=4.5cm
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