A flat coil of wire is used with an LC-tuned circuit as a receiving antenna. The coil has a radius of 0.30 m and consists of 420 turns. The

Question

A flat coil of wire is used with an LC-tuned circuit as a receiving antenna. The coil has a radius of 0.30 m and consists of 420 turns. The transmitted radio wave has a frequency of 1.3 MHz. The magnetic field of the wave is parallel to the normal of the coil and has a maximum value of 1.7 x 10-13 T. Using Faraday’s Law of electromagnetic induction and the fact that the magnetic field changes from zero to its maximum value in one-quarter of a wave period, find the magnitude of the average emf induced in the antenna in this time.

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Thu Thảo 4 weeks 2021-08-31T14:50:59+00:00 1 Answers 0 views 0

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    2021-08-31T14:51:59+00:00

    Answer:

    The average  emf induce is   V  = 2.625 * 10^{-5} \ V

    Explanation:

    From the question we are told that

      The radius of the coil is  r =  0.30 \ m

       The number of turns is  N  = 420  \ turns

        The frequency of the transition radio wave is  f = 1.3\ MHz = 1.3 *10^{6} Hz

         The magnetic field is  B_,{max} = 1.7 * 10^{-13} \ T

         The time taken for the magnetic field to go from zero to maximum is \Delta T = \frac{T}{4}

         

    The period of the transmitted radio wave is  T  = \frac{1}{f}

        So  

                  \Delta  T =  \frac{T}{4}  =  \frac{1}{4 f}

     The potential difference can be mathematically represented as

                   V = NA (\frac{\Delta B}{\Delta T} )

               V = NA ([B_{max}  - B_{min} ] * 4f)

    Where  B_{min} = 0T

    substituting values

                       V  =  420 * (\pi *(0.30)^2) * (1.7 *10^{-13} * 4 * 1.3 *10^{6})

                      V  = 2.625 * 10^{-5} \ V

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