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11 October, 13:12

A wire 2.80 m in length carries a current of 4.00 A in a region where a uniform magnetic field has a magnitude of 0.250 T. Calculate the magnitude of the magnetic force on the wire assuming the following angles between the magnetic field and the current.

(a) 60.0°

(b) 90.0°

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  1. 11 October, 13:40
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    (a) 2.425 N

    (b) 2.8 N

    Explanation:

    (a)

    The force on wire carrying current in a magnetic field is given as,

    F = BILsinФ ... Equation 1

    Where F = magnetic force on the wire, B = Magnetic Field, I = Current, L = Length, Ф = angle between the magnetic Field and the current.

    Given: B = 0.25 T, L = 2.8 m, I = 4 A, Ф = 60°

    Substitute into equation 1

    F = 0.25 (4) (2.8) sin60°

    F = 2.8*0.866

    F = 2.425 N.

    (b)

    Similarly,

    F = BILsinФ

    Given: B = 0.25 T, L = 2.8 m, I = 4 A, Ф = 90°.

    Substitute into the equation above

    F = 0.25 (2.8) (4) sin90°

    F = 2.8 (1)

    F = 2.8 N
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