Two infinitely long, straight wires are parallel and separated by a distance of one meter. They carry currents in the same direction. Wire 1

Question

Two infinitely long, straight wires are parallel and separated by a distance of one meter. They carry currents in the same direction. Wire 1 carries 4 times the current as wire 2 does. Determine the perpendicular distance from wire 1 to a point where the net magnetic field is zero between the two wires.

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Helga 2 months 2021-08-04T12:28:37+00:00 1 Answers 5 views 0

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    2021-08-04T12:30:31+00:00

    Answer:

    Explanation:

    magnetic field due to a current carrying infinite wire

    B = μ₀ / 4π x (2i / r )

    i is current , r is perpendicular distance of point from the wire

    Let at a point d distance away fro wire 1 , field is zero , let the current in wire 1 and 2 be 4i and i .

    between them at any point  field will be in opposite direction .

    magnetic field due to wire 1

    B₁ = μ₀ / 4π x (2i / r )

    = 10⁻⁷ x 2 x 4i / d

    magnetic field due to wire 2

    B₂ = μ₀ / 4π x (2i / r )

    = 10⁻⁷ x 2 x i / ( 1 – d )

    for zero field

    B₁ =B₂

    10⁻⁷ x 2 x 4i / d  = 10⁻⁷ x 2 x i / ( 1 – d )

    4 / d = 1 /( 1 – d )

    4 ( 1 – d ) = d

    4 -4d = d

    4 = 5d

    d = 4 / 5

    = .8 m

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