Question

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.

Answer 1

Faraday's law states that induced emf is directly proportional to the time rate of change of magnetic flux.
Lenz Law states - The induced current's magnetic field opposes the change in the magnetic flux that induced the current.
Emf = ΔϕB/Δt

For example, if the magnetic flux through a loop increases, the induced magnetic field is directed opposite to the"parent" magnetic field, thus countering the increase in flux. If the flux decreases, the induced current's magnetic field has the same direction as the parent magnetic field, thus countering the decrease in flux.

Changes that would induce an electromotive force (emf) in the loop =
1.)
The magnitude of B increases.
The magnitude of B decreases.
The loop rotates about the vertical axis (vertical dotted line).
The loop rotates about the horizontal axis (horizontal dotted line).

2.)

Flux ΦB through the loop = B* Area of loop
ΦB = B*xy

3.)
Induced Emf, E = ΔϕB/Δt
E = B*xy/t

4.)
If Magnetic field decreases , Current will be induced in a direction which will in increase the Magnetic field in downward direction.

Using Right hand thumb rule -
Direction of the induced current is = Counterclockwise

5.)
E = I*R
I = E/R
I =  B*xy/t*R

Magnitude I of the induced current, I =  Bxy/tR