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12 October, 14:55

An isolated conducting sphere has a 16 cm radius. One wire carries a current of 1.0000020 A into it. Another wire carries a current of 1.0000000 A out of it. How long would it take for the sphere to increase in potential by 1260 V?

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  1. 12 October, 18:46
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    It takes 11.20 ms for the sphere to increase in potential by 1260 V

    Explanation:

    Using the formula q = It where I is current in Ampere, and t is in seconds

    q = (1.000002 - 1.0000000) t

    q = 0.000002t

    Voltage on the surface of the sphere V = Kq / r

    where K is 9.0 * 10⁹ N². m² / c² and

    R = 16 cm = 16 / 100 = 0.16m

    V = Kq / r

    substitute the value into q

    V = K (0.000002t) / r

    cross multiply

    rV = K * 0.000002t

    make t subject of the formula

    t = 0.16 * 1260 / (9*10⁹ * 0.000002)

    t = 201.6 / (18 * 10³)

    t = 0.0112 s

    = 11.20 ms

    It takes 11.20 ms for the sphere to increase in potential by 1260 V
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