Inductive charging is used to wirelessly charge electronic devices ranging from toothbrushes to cell phones. Suppose the base unit of an ind

Question

Inductive charging is used to wirelessly charge electronic devices ranging from toothbrushes to cell phones. Suppose the base unit of an inductive charger produces a 1.50 ✕ 10−3 T magnetic field. Varying this magnetic field magnitude changes the flux through a 16.0-turn circular loop in the device, creating an emf that charges its battery. Suppose the loop area is 2.75 ✕ 10−4 m2 and the induced emf has an average magnitude of 5.30 V. Calculate the time required (in s) for the magnetic field to decrease to zero from its maximum value.

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Thu Nguyệt 5 years 2021-08-17T13:30:47+00:00 1 Answers 121 views 0

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  1. Maris
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    2021-08-17T13:32:38+00:00
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    Answer:

    The time required for the magnetic field to decrease to zero from its maximum value is 1.24 \times 10^{-6} sec.

    Explanation:

    Given :

    Magnetic field B = 1.5 \times 10^{-3} T

    No. of turns N = 16

    Area of loop A = 2.75 \times 10^{-4} m^{2}

    Average emf  =5.3 V

    From the faraday’s electromagnetic induction principle,

    Average emf = -N \frac{\Delta \phi}{\Delta t}

    Where \Delta \phi = change in magnetic flux, \Delta t = change in time.

    The magnetic flux is given by,

      \Delta \phi = BA

    In our example, we have to find time required to decrease magnetic field so our above equation is modified as,

     \Delta \phi = -BA

    (-) for decrease in magnetic field.

      \Delta t = \frac{NBA}{5.30}

    Where \Delta t = time required for the magnetic field to decrease to zero from its maximum value

      \Delta t = \frac{1.5 \times 10^{-3} \times 2.75 \times 10^{-4}\times 16 }{5.30}

           = 1.24 \times 10^{-6} sec.

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