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8 April, 22:23

A particle of charge q moves in a circle of radius a with speed v. Treat the circular path as a current loop with a constant current equal to the ratio of the particles charge magnitude to its period of motion. Find the maximum possible magnitude of the torque produced on the loop by a uniform magnetic field of magnitude B. (Use any variable or symbol stated above as necessary. Assume all quantities are in SI units.)

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  1. 9 April, 02:19
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    The magnitude is 6.87 * 10^-26N. m

    Explanation:

    There are missing details in this question.

    To solve this question, I'll assume the values of radius, speed and the magnitude of magnetic speed.

    Let r = radius = 5.3 * 10^-11m

    Let v = speed = 2.2 * 10^6 m/s

    Magnitude = 7.0mT

    First, we'll calculate the period of the motion ...

    This is calculated using 2πr/v

    T = 2 * π * 5.3 * 10^-11/2.2 * 10^6

    T = 1.513676460365E-16

    I = 1.514 * 10^-16

    Then we calculate the current.

    Current, I = e/T where T = 1.69 * 10^-19

    So I = 1.69 * 10^-19/1.514 * 10^-16

    I = 0.001116248348745

    I = 0.001112 A

    Next we calculate area

    Area = πr²

    Area = π (5.3 * 10^-11) ²

    Area = 8.824733763933E-21

    Area = 8.825E-21 m²

    Lastly, the maximum magnitude produced by the torque is calculated as:.

    i * Area * Magnitude

    0.001112 * 8.825 * 10^-21 * 7 * 10^-3

    6.86938E-26.

    Hence, the magnitude is 6.87 * 10^-26N. m
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