Three long, straight electrical cables, running north and south, are tightly enclosed in an insulating sheath. One of the cables carries a 2

Question

Three long, straight electrical cables, running north and south, are tightly enclosed in an insulating sheath. One of the cables carries a 22.3 A current southward; the other two carry currents of 18.9 A and 8.6 A northward.
Use Ampere’s law to calculate the magnitude of the magnetic field at a distance of 10.0 \rm m from the cables.

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Kiệt Gia 2 months 2021-07-24T05:27:39+00:00 2 Answers 2 views 0

Answers ( )

    0
    2021-07-24T05:29:12+00:00

    Answer:

    The resultant magnetic field is -1.04×10⁻⁷T

    Explanation:

    Given:

    i₁ = current through the first wire = 22.3 A (south)

    i₂ = current through the second wire = 18.9 A (north)

    i₃ = current through the third wire = 8.6 A (north)

    R = distance from the cables = 10 m

    The magnetic field through the first wire is equal:

    B_{1} =\frac{\mu _{o}i_{1}  }{2\pi R} =\frac{4\pi x10^{-7}*22.3 }{2\pi 10} =4.46x10^{-7} T

    The magnetic field through the second wire is equal:

    B_{2} =\frac{\mu _{o}i_{2}  }{2\pi R} =\frac{4\pi x10^{-7}*18.9 }{2\pi 10} =3.78x10^{-7} T

    The magnetic field through the third wire is equal:

    B_{3} =\frac{\mu _{o}i_{3}  }{2\pi R} =\frac{4\pi x10^{-7}*8.6 }{2\pi 10} =1.72x10^{-7} T

    The resultant magnetic field is equal:

    B=B_{1} -B_{2} -B_{3} =4.46x10^{-7} -3.78x10^{-7} -1.72x10^{-7} =-1.04x10^{-7} T

    0
    2021-07-24T05:29:34+00:00

    Answer:

    1.04 * 10^{-7} T

    Explanation:

    By using Ampere’s law formula we have:

    B = \frac{\mu_0 I}{2\pi r}

    where \mu_0 = 4\pi10^{-7} Tm/A is the permeability constant. r = 10 m is the distance from the wire, and I is the current magnitude. As there are 2 wires carrying currents northward and 1 carrying current southward:

    B = \frac{\mu_0 I_{N1}}{2\pi r} + \frac{\mu_0 I_{N2}}{2\pi r} - \frac{\mu_0 I_{S}}{2\pi r}

    B = \frac{\mu_0}{2\pi r}(I_{N1} + I_{N2} - I_S)

    B = \frac{4 \pi 10^{-7}}{2\pi *10}(18.9 + 8.6 - 22.3) = 1.04 * 10^{-7} T

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