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27 March, 00:20

A 113 ‑turn circular coil of radius 2.71 cm and negligible resistance is immersed in a uniform magnetic field that is perpendicular to the plane of the coil. The coil is connected to a 10.3 Ω resistor to create a closed circuit. During a time interval of 0.153 s, the magnetic field strength decreases uniformly from 0.441 T to zero. Find the energy, in millijoules, that is dissipated in the resistor during this time interval.

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  1. 27 March, 03:47
    0
    357 mJ

    Explanation:

    Parameters given:

    Number of turns, N = 113

    Radius, r = 2.71 cm = 0.0271 m

    Resistance connected to coil, R = 10.3 ohms

    Time interval, dt = 0.153 s

    Change in magnetic field, dB = 0 - 0.441 T = - 0.441 T

    First, we need to find the induced EMF in the coil. It is given as:

    V = - (N * A * dB) / dt

    A = area of coil = pi * r² = 3.142 * 0.0271² = 0.0023 m²

    Therefore:

    V = - (113 * 0.0023 * - 0.441) / 0.153

    V = 0.75 V

    Electrical energy dissipated in the resistor is given as:

    E = V² / (R * t)

    Where t is the time (0.153 secs)

    E = (0.75²) / (10.3 * 0.153)

    E = 0.357 J = 357 mJ

    The energy dissipated in the resistor is 357 mJ
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