A loop of wire with cross-sectional area 2 m2 is inserted into a uniform magnetic field with initial strength 2 T. The field is parallel to

Question

A loop of wire with cross-sectional area 2 m2 is inserted into a uniform magnetic field with initial strength 2 T. The field is parallel to the axis of the loop. The field begins to grow with time at a rate of 2 Teslas per hour. What is the magnitude of the induced EMF in the loop of wire

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Thiên Ân 3 years 2021-08-17T15:16:16+00:00 1 Answers 22 views 0

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  1. giabao
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    2021-08-17T15:17:47+00:00
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    Answer:

    The magnitude of the induced emf in the loop of wire, e = 0.00112 V

    Explanation:

    Cross Sectional Area of the loop, A = 2 m²

    Magnetic Field Strength, B = 2 T

    Rate of change of magnetic field strength, dB/dt = 2 T/hr

    dB/dt = 2 * 1/3600

    dB/dt = 0.00056 T/s

    The induced emf is given by the equation: e = \frac{d \phi}{dt}

    \phi = BA

    Differentiating both sides with respect to t

    \frac{d \phi}{dt} = \frac{d(BA)}{dt}\\\\\frac{d \phi}{dt} = A \frac{dB}{dt}

    Since  e = \frac{d \phi}{dt}

    e = A \frac{dB}{dt}\\\\e = 2 * 0.00056\\\\e = 0.00112 V

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