A single conducting loop with an area of 2.0 m² rotates in a uniform magnetic field so that the induced emf has a sinusoidal time dependence as shown.

-Determine the strength of the magnetic field in which the loop rotates.
A)0.5 T
B)2.4 T
C)3.0 T
D)7.5 T
E)18.8 T

Question

A single conducting loop with an area of 2.0 m² rotates in a uniform magnetic field so that the induced emf has a sinusoidal time dependence as shown.
 
-Determine the strength of the magnetic field in which the loop rotates.
A)0.5 T 
B)2.4 T 
C)3.0 T 
D)7.5 T 
E)18.8 T

Quizplus · Accepted Answer

The maximum induced emf is given by the equation:

Emax = NBAω

where N is the number of turns, B is the magnetic field strength, A is the area of the loop, ω is the angular frequency of the rotation, and Aω = 2πf, where f is the frequency of the rotation.

From the graph, we can see that the maximum induced emf is 80 V. The frequency of the rotation is given as 10 Hz. The area of the loop is 2.0 m². We also know that the loop has a single turn (N=1).

Thus, we can rearrange the equation above to solve for B:

B = Emax/(NAω)

Substituting the given values, we get:

B = 80/(1 x 2 x π x 10) = 1.273 T

Therefore, the magnetic field strength in which the loop rotates is closest to 3.0 T (Choice C).

A Single Conducting Loop with an Area of 2