A flexible, circular conducting loop of radius 0.15 m and resistance 4.0 $\varOmega$ lies in a uniform magnetic field of 0.25 T. The loop is pulled on opposite sides by equal forces and stretched until its enclosed area is essentially zero m 2 , as suggested in the drawings. It takes 0.30 s to close the loop. -Determine the magnitude of the emf induced in the loop. A)1.2 × 10^-¹ V B)1.8 × 10^-² V C)1.8 × 10² V D)5.9 × 10^-² V E)5.9 × 10²V

Question

Quizplus · Accepted Answer

The emf induced in the loop can be found using Faraday's Law:

emf = -N*d(Φ)/dt

where N is the number of turns in the loop and Φ is the magnetic flux through the loop.

Since the loop is stretched until its enclosed area is essentially zero, the magnetic flux through the loop will also be zero. Therefore, the emf induced in the loop is also zero.

However, the loop is not at rest during the stretching process, so there will be an induced emf due to the motion of the loop. This emf can be found using Faraday's Law again:

emf = -d(Φ)/dt

where Φ is the magnetic flux through the loop. Since the loop is circular and the magnetic field is uniform, we can use the equation for the magnetic flux through a loop:

Φ = B*A*cos(θ)

where B is the magnetic field, A is the area of the loop, and θ is the angle between the magnetic field and the normal to the loop. Since the loop is being stretched until its enclosed area is essentially zero, we can assume that the angle between the magnetic field and the normal to the loop is 90 degrees. Then,

Φ = 0

and

emf = -d(Φ)/dt = 0

Therefore, the emf induced in the loop is zero. None of the answer choices are correct.

A Flexible, Circular Conducting Loop of Radius 0 Ω\varOmegaΩ Lies in a Uniform Magnetic Field of 0

A Flexible, Circular Conducting Loop of Radius 0 $\varOmega$ Lies in a Uniform Magnetic Field of 0