Lenz's Law and Current's Direction

In summary, the correct diagram for the direction of the resultant induced current in the loop is (3) with a counter-clockwise current in the +z-direction. This is in accordance with Lenz's Law, which states that there will be an opposition to the change in magnetic flux, resulting in a counter-clockwise current.
  • #1
Soaring Crane
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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

tip30.gif


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.
 
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  • #2
Exactly right.
 
  • #3


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.
 

1. What is Lenz's Law?

Lenz's Law is a fundamental law of electromagnetism that states that the direction of an induced current will be such that it opposes the change that produced it. It is named after the physicist Heinrich Lenz who first described it in 1834.

2. How does Lenz's Law relate to electromagnetic induction?

Lenz's Law is directly related to electromagnetic induction, which is the process by which a changing magnetic field induces an electric current in a conductor. According to Lenz's Law, the induced current will always flow in a direction that opposes the change in the magnetic field that caused it.

3. What is the significance of Lenz's Law?

Lenz's Law is significant because it is a fundamental law of nature that helps us understand and predict the behavior of electromagnetic systems. It is also important in applications such as generators, motors, and transformers, where electromagnetic induction is used to convert between electrical and mechanical energy.

4. How is Lenz's Law related to the conservation of energy?

Lenz's Law is related to the conservation of energy because it ensures that the induced current will always oppose the change in the magnetic field that caused it. This means that energy is required to maintain the current, which comes from the change in the magnetic field. Therefore, Lenz's Law helps to ensure that energy is conserved in electromagnetic systems.

5. Can Lenz's Law be used to determine the direction of an induced current?

Yes, Lenz's Law can be used to determine the direction of an induced current. The direction of the induced current will always be such that it opposes the change in the magnetic field that caused it. This means that the induced current will flow in a direction that creates a magnetic field that opposes the original change in the magnetic field.

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