SP 15The magnetic field in a region of space is measured to be:This field is known to be caused by a cluster of long-straight wires that are

Question

SP 15The magnetic field in a region of space is measured to be:This field is known to be caused by a cluster of long-straight wires that are parallel to the z-axis. Find how much and in which direction the net current is flowing through the wires that pass through the rectangle whose corners are positioned at these points in the x, y plane: (0 cm, 0 cm), (2 cm, 3 cm), (3 cm, 0 cm)

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MichaelMet 4 years 2021-09-05T08:47:14+00:00 1 Answers 7 views 0

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  1. minhkhue
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    2021-09-05T08:49:13+00:00
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    Answer:

     i = 0.477 10⁴ B

    the current flows in the  counterclockwise

    Explanation:

    For this exercise let’s use the Ampere law

                        ∫ B . ds = μ₀ I

    Where the path is closed

    Let’s start by locating the current vines that are parallel to the z-axis, so it must be exterminated along the x-axis and as the specific direction is not indicated, suppose it extends along the y-axis.

    From BiotSavart’s law, the field must be perpendicular to the direction of the current, so the magnetic field must go in the x direction.

    We apply the law of Ampere the segment parallel to the x-axis is the one that contributes to the integral, since the other two have an angle of 90º with the magnetic field

    Segment on the y axis

            L₀ = (y2-y1)

            L₀ = 3-0 = 3 cm

    Segment on the point x = 2 cm

            L₁ = 3-0

            L₁ = 3cm

           B L = μ₀ I

           B 2L = μ₀ I

            i = 2 L B /μ₀

            i= 2 0.03 / 4π 10⁻⁷   B

            i = 4.77 10⁴  B

    The current is perpendicular to the magnetic field whereby the current flows in the  counterclockwise

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