PHYS 2212 Module 9 Class Activities

Lenz’s Law

I. Induced Currents

A. A copper wire loop is placed in a uniform magnetic field as shown. Determine whether there would be a current through the wire of the loop in each case below. Explain your answer in terms of magnetic forces exerted on the charges in the wire of the loop.

• The loop is stationary
• The loop is moving to the right.
• The loop is moving to the left.

B. Suppose that the loop is now placed in the magnetic field of a solenoid as shown.

1. Determine whether there would be a current through the wire of the loop in each case below. If so, give the direction of the current. Explain in terms of magnetic forces exerted on the charges in the wire of the loop.

• The loop is stationary
• The loop is moving toward the solenoid.
• The loop is moving away from the solenoid.

2. For each case above in which there is an induced current, determine:

• the direction of the magnetic moment of the loop. (Hint: Find the direction of the magnetic field at the center of the loop due to the induced current in the loop. The magnetic moment is a vector that points in this same direction.)
• whether the loop is attracted toward or repelled from the solenoid .
• whether the force exerted on the loop tends to increase or to decrease the relative motion of the loop and solenoid .

C. In each of the diagrams below, the position of a loop is shown at two times: t0 and t0 + t. The loop starts from rest in each case and is displaced to the right in Case A and to the left in Case B. On the diagrams indicate:

• the direction of the induced current through the wire of the loop,
• the magnetic moment of the loop,
• an area vector for each loop,
• the sign of the flux due to the external magnetic field (at both instants), and
• the sign of the induced flux (at both instants).

D. State whether you agree or disagree with each of the students below . If you agree, explain why . If you disagree, cite a specific case for which the student’s statement does not give the correct answer. (Hint: Consider cases A and B above.)

“The magnetic field due to the loop always opposes the external magnetic field. “

Student 1

“The flux due to the loop always has the opposite sign as the flux due to the external magnetic field. “

Student 2

“The flux due to the loop always opposes the change in the flux due to the external magnetic field.”

Student 3

Check in with an LA or instructor before proceeding.

II. Lenz’s Law

A. The diagram at right shows a stationary copper wire loop in a uniform magnetic field. The magnitude of the field is decreasing with time.

1. Would you predict that there would be a current through the loop:

• if you were to use the idea that there is a magnetic force exerted on a charge moving in a magnetic field? Explain your reasoning.
• if you were to use the reasoning of the student in part D of section I with whom you agreed? Explain.

2. It is observed that there is an induced current through the wire loop in this case. Use the appropriate reasoning above to find the direction of the current through the wire of the loop.

To understand the interaction between the wire loops and solenoids in section I, we can use the idea that a force is exerted on a charged particle moving in a magnetic field. In each of those cases there was an induced current when there was relative motion between the solenoid and the wire loop. In other situations such as the one above, however, there is an induced current in the wire loop even though there is no relative motion between the wire loop and the solenoid. There is a general rule called Lenz ‘ law that we can use in all cases to predict the direction of the induced current.

B. Discuss the statement of Lenz’s law in your textbook with your partners. Make sure you understand how it is related to the statement by the student with whom you agreed in part D of section I .

Check in with an LA or instructor before proceeding.

C. A wire loop moves from a region with no magnetic field into a region with a uniform magnetic field pointing into the page.

The loop is shown at two instants in time: t0 and t0 + t.

1. Is the magnetic flux through the loop due to the external field positive, negative, or zero:

• at t = t0?
• at t = t0 + t?

2. Is the change in flux due to the external field in the interval t positive, negative, or zero?

3. Use Lenz’ law to determine whether the flux due to the induced current in the loop is positive, negative, or zero.

4. What is the direction of the current in the loop during this time interval?

D. At two later instants, t = t1 and t = t1 + t, the loop is located as shown .

1. Use Lenz’s law to determine whether the flux due to the current induced in the loop is positive, negative, or zero. Explain.

2. Describe the current in the loop during this time interval.

3. Consider the following student dialogue:

Do you agree with either student? Explain. Check in with an LA or instructor before completing the activity.