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9 July, 11:40

A very long, straight solenoid with a cross-sectional area of 1.90 cm2 is wound with 86.6 turns of wire per centimeter. Starting at t = 0, the current in the solenoid is increasing according to i (t) = (0.176 A/s2) t2. A secondary winding of 5.0 turns encircles the solenoid at its center, such that the secondary winding has the same cross-sectional area as the solenoid. What is the magnitude of the emf induced in the secondary winding at the instant that the current in the solenoid is 3.2A?

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  1. 9 July, 15:15
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    |Emf| = 1.58x10⁻⁵ V

    Explanation:

    N = 88.6 turns/cm

    N = 8860 turns/metre

    The field inside the long solenoid is given by

    B = μ₀Ni

    B = 4πx10⁻⁷ x 8860 x 0.1761t² =

    B = 1.96x10⁻³ t²

    dB/dt = 3.92x10⁻³ t

    A = 1.90cm² = 1.90x10⁻⁴ m²

    |Emf| = rate of change of flux linkage

    |Emf| = d (NAB) / dt

    |Emf| = NA dB/dt

    |Emf| = 5 x 1.90x10⁻⁴ * 3.92x10⁻³ t

    |Emf| = 3.724x10⁻⁶ t

    if T is the time at which the current = 3.2A

    3.2 A = 0.176T²

    T = 4.26s

    |Emf| = 3.724x10⁻⁶t * 4.26s

    |Emf| = 1.58x10⁻⁵ V
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