Question

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

Answer 1

dB / dt = -141.47 T / s

Step-by-step 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