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14 June, 15:20

A piece of wire is bent to form a circle with radius r. It has a steady current I flowing through it in a counterclockwise direction as seen from the top (looking in the negative z-direction).

What is Bz (0), the z component of B at the center (i. e., x=y=z=0) of the loop?

Express your answer in terms of I, r, and constants like μ0 and π.

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  1. 14 June, 15:29
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    B=μ₀I/2r

    Explanation:

    Produced magnetic field due to an existing electric field through a coil or conductor can be explained by Biot-Savart Law. Formula for this law is:

    dB = (μ₀I/4π. r²) dL

    Here,

    r=Radius of the loop

    I and r are constants with respect to length L.

    To convert linear displacement L into angular displacement Ф:

    dL=r. dФ

    So,

    dB = (μ₀I/4π. r²) r. dФ

    dB = (μ₀I/4π. r) dФ

    Integrating both sides over the circle i. e. from 0 radians to 2π radians (360⁰), while the integration will apply only on dФ as all others are constants.

    B = (μ₀I/4πr) (2π-0)

    B = (μ₀I/2r)
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