Two concentric current loops lie in the same plane. The smaller loop has a radius of 2.9 cm and a current of 12 A. The bigger loop has a cur

Question

Two concentric current loops lie in the same plane. The smaller loop has a radius of 2.9 cm 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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Nho 5 years 2021-08-22T23:05:20+00:00 2 Answers 20 views 0

Answers ( )

  1. kimchi2
    0
    2021-08-22T23:06:59+00:00
    Reply

    Answer:

    The radius is 4.833cm

    Explanation:

    The image will provide a better clarification of the explanation

  2. phucdien
    0
    2021-08-22T23:06:59+00:00
    Reply

    Answer:

    the radius of bigger loop is 4.83cm

    Explanation:

    Given that,

    two concentric current loops

    smaller loop radius = 2.9 cm

    current in smaller loop = 12 A

    current in the bigger loop = 20 A

    magnetic field at the center of loop = 0

    Radius of the bigger loop = ?

    The equation for the magnetic field at the center of a circular loop is:

    B=\frac{\mu_0I}{2R}

    we have:

    B = B_1 + B_20 = \dfrac{\mu_0I_1}{2R_1} +\dfrac{\mu_0I_2}{2R_2}

    now,

    \dfrac{I_1}{R_1} = \dfrac{I_2}{R_2}R_2 = I_2\dfrac{R_1}{I_1} = 20\times \dfrac{2.9}{12} = 4.83 cm

    the radius of bigger loop is 4.83cm

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