A long wire carrying I=1.3A of constant current oriented East-to-West (and the current is running eastwards) is placed distance d=0.8cm over

Question

A long wire carrying I=1.3A of constant current oriented East-to-West (and the current is running eastwards) is placed distance d=0.8cm over the top of a compass needle. Assuming the Earth magnetic field to be BEarth= 29μT what is the absolute value of the angular deviation θ of the compass needle from the North-to-South direction?

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Thanh Thu 4 years 2021-08-04T22:44:05+00:00 1 Answers 66 views 0

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  1. danthu
    0
    2021-08-04T22:45:53+00:00
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    Answer:

    Explanation:

    Magnetic field due to a long wire

    = 10⁻⁷ x 2i / r where i is current in the wire and r is distance of the point from the wire

    In the given case magnetic field

    B = 10⁻⁷ x 2i / r

    = 10⁻⁷ x 2x 1.3 / .8 x 10⁻²

    = 3.25 x 10⁻⁵ T

    = 32.5 x 10⁻⁶ T

    It will create a deflecting torque on the compass needle

    Let after turning by angle θ , equilibrium point is reached

    at this point , deflecting torque = restoring torque by earth’s magnetic field

    MB cosθ = MHsinθ , M is magnetic moment of magnetic needle , H is horizontal component of earth’s magnetic field.

    Tanθ = B / H

    = 32.5 / 29

    =1.20

    θ = 50 degree approx .

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