A hollow cylinder with an inner radius of and an outer radius of conducts a 3.0-A current flowing parallel to the axis of the cylinder. If t

Question

A hollow cylinder with an inner radius of and an outer radius of conducts a 3.0-A current flowing parallel to the axis of the cylinder. If the current density is uniform throughout the wire, what is the magnitude of the magnetic field at a point from its center?

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RobertKer 3 months 2021-08-17T01:49:07+00:00 1 Answers 4 views 0

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    2021-08-17T01:50:11+00:00

    Complete Question:

    A hollow cylinder with an inner radius of 4.0mm and an outer radius of 30mm conducts a 3.0-A current flowing parallel to the axis of the cylinder. If the current density is uniform throughout the wire, what is the magnitude of the magnetic field at a point 12mm from its center?

    Answer:

    The magnitude of the magnetic field = 7.24 μT

    Explanation:

    Inner radius, a = 4.0 mm = 0.004 m

    Outer radius, b = 30 mm = 0.03 m

    Radius, r = 12 mm = 0.012 m

    let h² = b² – a²

    h² = 0.03² – 0.004²

    h² = 0.000884

    Let d² = r² – a²

    d² = 0.012² – 0.004²

    d² = 0.000128

    Current I = 3A

    μ = 4π * 10⁻⁷

    The magnitude of the magnetic field is given by:

    B = \frac{\mu I d^{2} }{2\pi r h^{2} } \\B =  \frac{4\pi * 10^{-7}   * 3* 0.000128^{2} }{2\pi *0.012* 0.000884^{2} }

    B = 7.24 * 10⁻⁶T

    B = 7.24 μT

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