Lenz's Law and Current's Direction

[Soaring Crane]

Homework Statement

A loop rests in the xy plane. The z axis is normal to the plane and positive upward. The direction of the changing flux is indicated by the arrow on the z axis. The diagram that correctly shows the direction of the resultant induced current in the loop is

a. (1)
b. (2)
c. (3)
d. (4)
e. (5)

Homework Equations

emf = - [d(magnetic flux)]/dt

The Attempt at a Solution

In Figure 4, the magnetic flux is increasing in the -z-direction. From Lenz's Law, there is an opposition to this change, so the induced current will be counter-clockwise, which corresponds to the +z-direction?

Thanks.

 

[Doc Al]

Exactly right.

 

[m2003]

Your understanding of Lenz's Law is correct. The correct diagram is option (3), where the induced current is flowing counter-clockwise in the loop, opposing the increase in magnetic flux in the -z-direction. This is because according to Lenz's Law, the induced current will always flow in a direction that creates a magnetic field that opposes the change in the external magnetic field. In this case, the external magnetic field is increasing in the -z-direction, so the induced current will flow in the +z-direction to create a magnetic field in the opposite direction. This is consistent with the equation you provided, where the induced emf is negative because it is opposing the change in magnetic flux.