Question

A coil with 275 turns and a cross-sectional area of 0.750 m^2 experiences a magnetic field whose strength increases by +0.900 T in 1.25 s. The plane of the coil is perpendicular to the plane of the magnetic field. What is the induced emf in the coil?

a) 159.375 V
b) 205.125 V
c) 225.000 V
d) 281.250 V

Answer 1

To determine the induced emf in a coil where magnetic field strength increases, Faraday's Law is used, resulting in an induced emf of 148.5 V.

Step-by-step explanation:

The question is asking to calculate the induced electromotive force (emf) in a coil due to some change in magnetic flux. To find this, we can use Faraday's Law of electromagnetic induction, which states that the induced emf in a coil is equal to the negative change in magnetic flux (ΔΦB) times the number of turns (N) in the coil, or emf = -N (ΔΦB/Δt). Because we are not asked for the direction and given that the field and area are perpendicular, we can ignore the negative sign and calculate the magnitude of emf directly.

The magnetic flux (ΦB) is the product of the magnetic field (B) and the cross-sectional area (A) that the field penetrates, so ΔΦB is B × A when the area and field are perpendicular. In this case, ΔΦB = 0.900 T × 0.750 m2 = 0.675 T·m2. The emf induced in the coil over the time interval of 1.25 s with 275 turns will then be emf = 275 turns × (0.675 T·m2/1.25 s) = 148.5 V.