Faraday’s Law and Induced EMF

The figure displays a rectangular loop of wire with sides x and y placed in a region where a uniform magnetic field ! exists. The resistance of the loop is R. Initially the field is perpendicular to the plane of the loop and is directed out of the page. The loop can rotate about either the vertical or horizontal axis, passing through the midpoints of the opposite sides, as shown.

1. Which of the following changes would induce an electromotive force (emf) in the loop? When you consider each option, assume that no other changes occur.

o The magnitude of B increases.
o The magnitude of B decreases.
o The loop rotates about the vertical axis (vertical dotted line) shown in the figure.
o The loop rotates about the horizontal axis (horizontal dotted line) shown in the figure.
o The loop moves to the right while remaining in the plane of the page.
o The loop moves toward you, out of the page, while remaining parallel to itself.

2. Find the flux ?B through the loop. Express your answer in terms of x, y, and B. Show your work.

3. If the magnetic field steadily decreases from B to zero during a time interval t, what is the magnitude of the induced emf? Express your answer in terms of x, y, B and t. Show your work.

4. If the magnetic field steadily decreases from B to zero during a time interval t, what is the direction of the induced current?

o Clockwise
o Counterclockwise

5. If the magnetic field steadily decreases from B to zero during a time interval t, what is the magnitude I of the induced current? Express your answer in terms of x, y, B, t and R. Show your work.