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26 January, 11:35

3) A ring of radius 15 cm is injected with an amount of charge of 3.5 * 10-12C, uniformly distributed along the ring. The ring rotates with an angular velocity of 17 rad/s. Find the power radiated by the system.

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  1. 26 January, 11:54
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    Given Information:

    Radius = r = 15 cm = 0.15 m

    Charge = q = 3.5x10⁻¹² C

    Angular velocity = ω = 17 rad/s

    Required Information:

    Power radiated = P = ?

    Answer:

    Power radiated = 1.987x10⁻¹² W

    Explanation:

    We know that power is given by

    P = VI

    Where V is the potential due to charge and is given by

    V = kq/r

    Where k is the coulomb constant 8.98x10⁹ N. m²/C²

    V = (8.98x10⁹*3.5x10⁻¹²) / 0.15

    V = 0.2095 V

    we know that the rate of charge flow is current

    I = q/t

    where t is found by the relation

    ω = 2π/t

    t = 2π/ω

    t = 2π/17

    t = 0.369 s

    so current is

    I = q/t = 3.5x10⁻¹²/0.369

    I = 9.485x10⁻¹² A

    Therefore, the amount of power radiated is

    P = VI

    P = 0.2095*9.485x10⁻¹²

    P = 1.987x10⁻¹² W
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