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27 September, 20:10

A 2.5 m - long wire carries a current of 8.0 A and is immersed within a uniform magnetic field B⃗. When this wire lies along the + x axis, a magnetic force F⃗ = (-2.3j) N acts on the wire, and when it lies on the + y axis, the force is F⃗ = (2.3i-5.6k) N.

Part A - Find the x-component of B⃗.

Part B - Find the y-component of B⃗.

Part C - Find the z-component of B⃗.

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  1. 27 September, 20:31
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    Let the magnetic field be B = B₁i + B₂j + B₃k

    Force = I (L x B), I is current, L is length and B is magnetic field.

    In the first case

    force = - 2.3 j N

    L = 2.5 i

    puting the values in the equation above

    - 2.3 j = 8 [ 2.5 i x (B₁i + B₂j + B₃k) ]

    = - 20 B₃ j + 20 B₂ k

    comparing LHS and RHS,

    20B₃ = 2.3

    B₃ =.115

    B₂ = 0

    In the second case

    L = 2.5 j

    Force = I (L x B)

    2.3i-5.6k = 8 (2.5 j x (B₁i + B₂j + B₃k)

    = - 20 B₁ k + 20B₃ i

    2.3i-5.6k = - 20 B₁ k + 20B₃ i

    B₃ =.115

    B₁ =.28

    So magnetic field B =.28 i +.115 B₃

    Part A

    x component of B =.28 T

    Part B

    y component of B = 0

    Part C

    z component of B =.115 T.
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