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 $\vec { B }$ field in 0.10 s.The coil has 60 turns and is perpendicular to the $\vec { B }$ 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

We can use Faraday's Law of Electromagnetic Induction to determine the average induced emf in the coil:

ε = -NΔΦ/Δt

where ε is the induced emf, N is the number of turns in the coil, ΔΦ is the change in magnetic flux through the coil, and Δt is the time for the change to occur.

In this case, the coil is dropped from a zero magnetic field position into a 1.4-T magnetic field, so the change in magnetic flux through the coil is:

ΔΦ = BA = (1.4 T)(0.08 m)(0.10 m) = 0.0112 T m^2

where B is the magnetic field strength, and A is the area of the coil.

Substituting the given values into the formula for induced emf, we get:

ε = -(60)(0.0112 T m^2)/(0.10 s) = -6.72 V

The negative sign indicates that the direction of the induced emf is opposite to the direction of the change in magnetic flux. Therefore, the average induced emf in the coil is:

|ε| = 6.72 V ≈ 6.7 V

So, the best choice is C, 6.7 V.

A Flat Rectangular Coil with Dimensions of 8 B⃗\vec { B }B

A Flat Rectangular Coil with Dimensions of 8 $\vec { B }$