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19 August, 00:16

A technician wearing a brass bracelet enclosing area 0.00500 m2 places her hand in a solenoid whose magnetic field is 4.50 T directed perpendicular to the plane of the bracelet. The electrical resistance around the circumference of the bracelet is 0.0200. An unexpected power failure causes the field to drop to 1.35 T in a time of 20.0 ms. (a) Find the current induced in the bracelet.

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  1. 19 August, 00:37
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    39.375 A

    Explanation:

    To find the induced current, we use the relation

    e = - ΔΦ/Δt, where

    ΔΦ = change in magnetic flux of the bracelet

    Δt = change in time, = 20 ms

    Also, Φ = A.ΔB, such that

    A = area of the bracelet, 0.005m²

    ΔB = magnetic field strength of the bracelet = 1.35 - 4.5 = - 3.15 T

    ΔΦ = A.ΔB

    ΔΦ = 0.005 * - 3.15

    ΔΦ = -.01575 wb

    e = - ΔΦ/Δt

    e = - 0.01575 / 20*10^-3

    e = 0.7875 V

    From the question, the resistance of the bracelet is 0.02 ohm, so

    From Ohms Law, I = V/R

    I = 0.7875 / 0.02

    I = 39.375 A
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