A 60 [Hz] high-voltage power line carries a current of 1000 [A]. The power line is at a height of 50 [m] above the earth. What is the magnit

Question

A 60 [Hz] high-voltage power line carries a current of 1000 [A]. The power line is at a height of 50 [m] above the earth. What is the magnitude of the magnetic field B [T] at a point on the surface of the earth directly below the power line

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King 4 years 2021-08-11T21:34:58+00:00 1 Answers 5 views 0

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  1. Bo
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    2021-08-11T21:36:27+00:00
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    Answer:

    The magnetic field 50m below the transmission line is 4 micro Tesla.

    Explanation:

    The magnetic field B due to a current carrying wire at a distance R is

    B = \dfrac{\mu_o I }{2\pi R }

    where \mu_o = 4\pi*10^{-7}H/m is the magnetic constant.

    For the case of the  power line we put in I = 1000A and R = 50m to get:

    B = \dfrac{(4\pi*10^{-7}) (1000A) }{2\pi (50m) }

    B = 4\mu T.

    Thus, the magnetic field 50m below the transmission line is 4 micro Tesla.

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