A flat rectangular coil with dimensions of 8.0 cm × 10 cm is dropped from a zero magnetic field position into a 1.4-T magnetic field in 0.10 s.The coil has 60 turns and is perpendicular to the magnetic field.What is the average induced emf in the coil as a result of this action?
A)8.6 V
B)2.4 V
C)6.7 V
D)3.6 V
E)0 V

Question

Quizplus · Accepted Answer

First, we need to find the magnetic flux through the coil. Since the coil is perpendicular to the magnetic field, the flux is simply the product of the magnetic field, the area of the coil, and the cosine of the angle between the field and the normal of the coil:
Φ = B*A*cos(0) = 1.4 T * (8.0 cm * 10 cm) * cos(0) = 112 mT m²

Next, we need to find the change in flux over the 0.10 s time interval. Since the coil is dropped from a zero field position, the initial flux is zero. The final flux is the same as above. Therefore, the change in flux is:
ΔΦ = 112 mT m² – 0 T m² = 112 mT m²

Finally, we can use Faraday's law to find the average induced emf:
ε = (N*ΔΦ)/Δt = (60*112 mT m²)/(0.10 s) = 672 mV
or, converting to volts,
ε = 0.672 V ≈ 6.7 V

Therefore, the best choice is C.

A Flat Rectangular Coil with Dimensions of 8