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29 August, 20:07

The current in a long solenoid of radius 6 cm and 17 turns/cm is varied with time at a rate of 5 A/s. A circular loop of wire of radius 8 cm and resistance 4 Ω surrounds the solenoid. Find the electrical current induced in the loop (in µA).

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  1. 29 August, 22:42
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    53.63 μA

    Explanation:

    radius of solenoid, r = 6 cm

    Area of solenoid = 3.14 x 6 x 6 = 113.04 cm^2 = 0.0113 m^2

    n = 17 turns / cm = 1700 / m

    di / dt = 5 A/s

    The magnetic field due to the solenoid is given by

    B = μ0 n i

    dB / dt = μ0 n di / dt

    The rate of change in magnetic flux linked with the solenoid =

    Area of coil x dB/dt

    = 3.14 x 8 x 8 x 10^-4 x μ0 n di / dt

    = 3.14 x 64 x 10^-4 x 4 x 3.14 x 10^-7 x 1700 x 5 = 2.145 x 10^-4

    The induced emf is given by the rate of change in magnetic flux linked with the coil.

    e = 2.145 x 10^-4 V

    i = e / R = 2.145 x 10^-4 / 4 = 5.36 x 10^-5 A = 53.63 μA
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