Understand Faraday's Law and Lenz' Law

In summary: It does affect whether there is a current in the ring.In summary, the presence or absence of a gap does not affect the induced emf around the ring, and the emf can be derived by integrating the E field over the ring perimeter. The direction of the emf can be determined by Lenz's law, regardless of whether the ring is complete or incomplete.
  • #1
christang_1023
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Homework Statement
1. Is Lenz's law applied only when there is a closed loop?
2. When a ring in a changing magnetic field is not complete (i.e. open circuit with a small gap), how to analyze the emf of the ring?
Relevant Equations
Shown below
242551

Above is an example figure.

2. When a ring in a changing magnetic field is not complete (i.e. open circuit with a small gap), how to analyze the emf of the ring?
According to the general form of Faraday's law, ## \oint \vec{E} \cdot d \vec{s} = -\frac{d \Phi}{dt} ##, I deduce that although it is not a closed loop, there is still emf within the incomplete ring conductor. How can I derive the emf of this ring?
 
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  • #2
The presence or absence of a gap does not affect the induced emf around the ring. It does affect whether there is a current in the ring.
 
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  • #3
christang_1023 said:
Problem Statement
1. Is Lenz's law applied only when there is a closed loop?
2. When a ring in a changing magnetic field is not complete (i.e. open circuit with a small gap), how to analyze the emf of the ring?
Relevant Equations
Shown below

View attachment 242551
Above is an example figure.

2. When a ring in a changing magnetic field is not complete (i.e. open circuit with a small gap), how to analyze the emf of the ring?
According to the general form of Faraday's law, ## \oint \vec{E} \cdot d \vec{s} = -\frac{d \Phi}{dt} ##, I deduce that although it is not a closed loop, there is still emf within the incomplete ring conductor. How can I derive the emf of this ring?
As you say, for a closed, finite-R ring the E field and emf (- to +) are in same direction as the current, which enables you to determine the direction of the emf by Lenz's law.

For a non-existing ring the emf is still in the same direction so you can pretend the ring is solid, the use Lez's law.

The emf is ∫E dl, the integral of the E field over the ring perimeter. If the E field were electrostatic (as in a resistor in a battery-resistor circuit) the potential difference or voltage (- to +) would be the NEGATIVE of ∫E dl.
 
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  • #4
jtbell said:
The presence or absence of a gap does not affect the induced emf around the ring.
Note that here, "induced emf" refers specifically to the emf that is induced by the changing B field via Faraday's Law. Depending on the situation, this might not be the only emf around the ring.
 

Related to Understand Faraday's Law and Lenz' Law

1. What is Faraday's Law?

Faraday's Law states that a changing magnetic field will induce an electromotive force (EMF) in a conductor.

2. What is Lenz' Law?

Lenz' Law states that the direction of the induced current in a conductor will oppose the change that caused it.

3. How are Faraday's Law and Lenz' Law related?

Faraday's Law and Lenz' Law are both fundamental principles in electromagnetism, and they are closely related. Faraday's Law explains how a changing magnetic field induces an EMF in a conductor, while Lenz' Law explains the direction of the induced current in relation to the change in the magnetic field.

4. How are Faraday's Law and Lenz' Law used in real life?

Faraday's Law and Lenz' Law are used in many real-life applications, such as generators, transformers, and motors. They are also essential in understanding how electricity is generated and distributed in power plants.

5. Can Faraday's Law and Lenz' Law be violated?

No, Faraday's Law and Lenz' Law are fundamental principles in electromagnetism and have been extensively tested and proven to be true. They cannot be violated under normal circumstances.

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