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9 October, 12:05

A 5 cm length of wire carries a current of 3 A in the positive z direction. The force on this wire due to a magnetic field vector is vector = (-0.2 ihatbold + 0.2 jhatbold) N. If this wire is rotated so that the current flows in the positive x direction, the force on the wire is vector = 0.2 khatbold N. Find the magnetic field vector.

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  1. 9 October, 13:18
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    B = 4/3 (i + j + k)

    Explanation:

    I = 3 k

    L = 5 x 10⁻² m

    F = - 0.2 i + 0.2 j

    Let magnetic field be B

    B = B₁ i + B₂ j + B₃ k

    F = L (I x B)

    = 5 x 10⁻² 3 k x (B₁ i + B₂ j + B₃ k)

    = 15 x 10⁻² B₁ j - 15 x 10⁻² B₂ i

    Given

    F = - 0.2 i + 0.2 j

    equating equal terms

    15 x 10⁻² B₂ =.2

    15 x 10⁻² B₁ =.2

    B₁ =.02 / 15 x 10⁻² = 20 / 15 N

    B₂ =.02 / 15 x 10⁻² = 20 / 15 N

    Now wire is rotated so that current flows in positive x direction

    I = 3 i

    F =. 2 k

    F = L (I x B)

    = 5 x 10⁻² x 3 i x (B₁ i + B₂ j + B₃ k)

    = 15 x 10⁻² B₃ k

    15 x 10⁻² B₃ =.2

    B₃ =.2 / 15 x 10⁻²

    B₃ = 20 / 15

    B = B₁ i + B₂ j + B₃ k

    20 / 15 9 (i + j + k)

    B = 4/3 (i + j + k)
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