A 100-turn coil has a radius of 7.50 cm and a resistance of 50.0 W. At what rate must a perpendicular magnetic field change to produce a current of 5.00 A in the coil

dB / dt = -141.47 T / s

Explanation:

For this exercise let's use Faraday's law to calculate the induced electromotive force

          E = - N dФ / dt

the magnetic flux is

         Ф = B. A

in this case the direction of the field and the normal to area are parallel so the scalar product is reduced to the algebraic product

         Ф = B A

  we substitute

        E = - N A dB / dt

the area of the loop is

        A = π r²

we substitute

          E = - N π r² dB / dt

in the exercise indicate that the resistance of the coil is R = 50.0 Ω,

           E = i R

we substitute

           i R = -N π r² dB / dt

           dB / dT = - i R / N π r²

let's calculate

           dB / dt = - 5.00 50.0 / (100 π 0.075²)

           dB / dt = -141.47 T / s

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