provides one model for solving this problem. The maximum strength of the earth’s magnetic field is about 6.9 x 10-5 T near the south magneti

Question

provides one model for solving this problem. The maximum strength of the earth’s magnetic field is about 6.9 x 10-5 T near the south magnetic pole. Suppose we want to utilize this field with a rotating coil to generate 84.5-Hz ac electricity What is the minimum number of turns (area per turn = 0.021 m2) that the coil must have to produce an rms voltage of 170 V?

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Thanh Hà 1 month 2021-08-05T10:28:55+00:00 1 Answers 2 views 0

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    2021-08-05T10:30:46+00:00

    Answer:

    The minimum no. of turns is 3.126 \times 10^{5}

    Explanation:

    Given:

    Magnetic field B = 6.9 \times 10^{-5} T

    Frequency f = 84.5 Hz

    Area of turn A = 0.021 m^{2}

    Voltage V_{rms}  = 170 V

    From the formula of induced emf,

    V = NBA \omega

    Where \omega = 2\pi f and V = \sqrt{2} V_{rms}

    So number of turn is,

    N = \frac{\sqrt{2} V_{rms} }{AB2\pi f }

    N = \frac{\sqrt{2} \times 170 }{0.021 \times 6.9 \times 10^{-5} \times 6.28 \times 84.5 }

    N = 3.126 \times 10^{5}

    Therefore, the minimum no. of turns is 3.126 \times 10^{5}

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