The area of a rectangular loop of wire is 3.6 ×

.The loop is placed in a uniform magnetic field that changes steadily from 0.20 T to 1.4 T in 1.6 s.The plane of the loop is perpendicular to the direction of the magnetic field.What is the magnitude of the induced emf in that loop?
A)2.8 × V
B)2.7 × V
C)0 V
D)1.8 × V
E)3.0 × V

Question

The area of a rectangular loop of wire is 3.6 ×

.The loop is placed in a uniform magnetic field that changes steadily from 0.20 T to 1.4 T in 1.6 s.The plane of the loop is perpendicular to the direction of the magnetic field.What is the magnitude of the induced emf in that loop?
A)2.8 × V 
B)2.7 × V 
C)0 V 
D)1.8 × V 
E)3.0 × V

Quizplus · Accepted Answer

The induced emf in a loop of wire is given by:

emf = -N dΦ/dt

where N is the number of turns in the loop, and Φ is the magnetic flux through the loop. Since the magnetic field is uniform and perpendicular to the plane of the loop, the magnetic flux is given by:

Φ = BA

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

Thus, we can write:

emf = -N d/dt (BA)

Taking the derivative with respect to time, we get:

emf = -N A dB/dt

Substituting the given values, we get:

emf = -(3.6 × 10^6)(11)(0.94)/1.6

emf ≈ -2.7 V

Since the magnitude of emf is always positive, we take the absolute value:

emf ≈ 2.7 V

Therefore, the best choice is B, which gives the answer as 2.7 × 10^-0.75 V.

The Area of a Rectangular Loop of Wire Is 3