Magnetic Flux & Current in a Dropped Magnet & Wire Loop

[Feodalherren]

Homework Statement

A bar magnet is held above the center of a wire loop lying in the horizontal plane, as shown in the figure below. The south end of the magnet is toward the loop. After the magnet is dropped, what is true of the current in the resistor as viewed from above? (Select all that apply.)

It is counterclockwise as the magnet falls toward the loop.
It is clockwise as the magnet falls toward the loop.
It is always clockwise.
It is clockwise after the magnet has moved through the loop and moves away from it.
It is first counterclockwise as the magnet approaches the loop and then clockwise after it has passed through the loop.

Homework Equations

Lenz's law and Faraday's Law

The Attempt at a Solution

This is my conceptual picture of what's going on.

As the magnet is falling in the field lines are going N to S as always. So Just at the moment when the bottom of the South pole of the magnets hits the area inside the circle the field lines are coming toward us (as viewed from the top). As the magnet falls through and the N side is facing us, the field lines are again, coming toward us.
In both cases the current will be induced in such a way that the magnetic flux through the surface is constant. So it seems to me that it should flow clockwise in both cases. This is, however, incorrect. Where am I going wrong?

 

[Orodruin]

The induced emf is proportional to the change in (i.e., time derivative of) the magnetic flux, not to the magnetic flux itself.

 

[Feodalherren]

Yes, that is what my pictures are trying to illustrate.

 

[Orodruin]

So how is the flux changing when the magnet falls into the loop? How is it changing when it falls out of the loop?

 

[HalfLostAndSearching]

Your conceptual picture is correct, but your understanding of Lenz's law and Faraday's law is slightly off. Lenz's law states that the direction of the induced current will always be such that it opposes the change in magnetic flux. In this case, as the magnet falls towards the loop, the magnetic flux through the loop increases, so the induced current will flow in such a way to oppose this increase. This means that the current will flow counterclockwise as the magnet approaches the loop, and then switch to flowing clockwise as the magnet passes through the loop and moves away from it.

Faraday's law states that the magnitude of the induced current is proportional to the rate of change of magnetic flux. This means that as the magnet falls towards the loop, the current will increase in magnitude, and then decrease as the magnet passes through the loop and moves away from it.

In summary, the correct answer to the question would be: "It is first counterclockwise as the magnet approaches the loop and then clockwise after it has passed through the loop."