# Induced EMF in a circle: Faraday's law

• Biker
In summary, there is a discussion about a loop in the form of a circle with a varying magnetic field inside. The participants discuss the application of Faraday's law and Lorentz force in this situation, as well as the relationship between magnetic field and emf. There is also a mention of the use of integration in finding the emf and the concept of flux rule. The conclusion is that the fundamental flux rule (E=dΦ/dt) holds in every case, whether the circuit is stationary or moving.
Biker

## Homework Statement

Explain what happens in the following situation:
You have a loop in the form of a circle and there is a varying magnetic field inside that loop as the following picture illustrates:

lorentez force

## The Attempt at a Solution

I first thought that there is a changing magnetic field inside the loop which is after all a change in flux. But using lorentz force clearly no magnetic field passing through the wires which means there shouldn't be any emf. How to reconcile between the two? Faraday's law requires the whole loop to be "Covered" by a magnetic field?

Then I started to think about a transformer, The magnetic field lines pass through the coils by what I have written above there must be an outside magnetic field acting on the wires themselves too. Isn't it weird that lorentz force depend on the magnetic field acting on the wire but faraday's law depend on the magnetic field passing through the whole loop?

Biker said:
Then I started to think about a transformer, The magnetic field lines pass through the coils by what I have written above there must be an outside magnetic field acting on the wires themselves too. Isn't it weird that lorentz force depend on the magnetic field acting on the wire but faraday's law depend on the magnetic field passing through the whole loop?
Motional emf and Faraday's law (the flux rule) give the same result.
Here's my recent thread about a different issue related to the same problem.
Hope it helps..

cnh1995 said:
Not sure I understood everything tbh, Especially the link that Dale put. Certainly I can't understand the math if I didnt even take integration (Such shame, next semster though).

Isn't your's a bit different? I mean the problem you had was about B not being strong enough to be equal to the change of magnetic flux which is certainly a problem ( I thought about similar things but I just gave up couldn't solve and pretty sure our exam level is just plug and chug with kind of ideas) Not sure what was the answer, didnt fully understand it because I don't know about reluctance.

Here in the example above there is certainly no magnetic field passing through the conductor.. Unless they spread out or something :/

This is equivalent to having a conductor long straight wire outside a magnetic field then making an imaginary circuit that includes some parts of a varying magnetic field and then saying there is an EMF inside a conductor

Biker said:
Here in the example above there is certainly no magnetic field passing through the conductor.. Unless they spread out or something
The wikipedia article has chosen a random shape for the example and hence they are using integration.
The flux rule is the fundamental rule. Whenever the flux linking with a loop changes, an emf is induced in the loop. This is true in every case, be it a stationary circuit (transformer) or a moving circuit (dc generator). In a moving circuit, the motional emf Blv is equal to rate of change of flux i.e. Blv=dΦ/dt.

cnh1995 said:
The wikipedia article has chosen a random shape for the example and hence they are using integration.
The flux rule is the fundamental rule. Whenever the flux linking with a loop changes, an emf is induced in the loop. This is true in every case, be it a stationary circuit (transformer) or a moving circuit (dc generator). In a moving circuit, the motional emf Blv is equal to rate of change of flux i.e. Blv=dΦ/dt.
So some how the magnetic field is stretching out to contain the conductor? Enough to make the motion emf equal to the flux rule?

Biker said:
So some how the magnetic field is stretching out to contain the conductor? Enough to make the motion emf equal to the flux rule?
In this circuit, the circuit is stationary and the flux is varying w.r.t time. This is exactly like a transformer.
In a moving circuit loop, what you write as motional emf Blv is actually dΦ/dt in disguise. The rate of change of flux in the moving loop is equal to the motional emf in the loop.
In your OP, the emf is induced as per the flux rule, which is true in any case, be it a stationary circuit (your OP) or a moving circuit. It's exactly like a transformer. The field is not stretching out to cut the conductor. It is simply varying w.r.t. time and that is enough to induce an emf. It's the fundamental flux rule (E=dΦ/dt) that holds in every case.

cnh1995 said:
In this circuit, the circuit is stationary and the flux is varying w.r.t time. This is exactly like a transformer.
In a moving circuit loop, what you write as motional emf Blv is actually dΦ/dt in disguise. The rate of change of flux in the moving loop is equal to the motional emf in the loop.
In your OP, the emf is induced as per the flux rule, which is true in any case, be it a stationary circuit (your OP) or a moving circuit. It's exactly like a transformer. The field is not stretching out to cut the conductor. It is simply varying w.r.t. time and that is enough to induce an emf. It's the fundamental flux rule (E=dΦ/dt) that holds in every case.
For the first problem, I meant only the conductor could move. Not the whole "Mathematical" circuit. Not sure how Blv could happen in disguise. I know that faraday's law is a general law and i have already used it to find the emf in a lot of shapes: circle...etc and if you integrate the magnetic field using lorentz force you will get the same.

The problem in the first problem is that there is no actually B acting on the conductor. So there is no reason to use lorentz force. However, I may accept that lorentz force works in only some condition but the flux rule is more general because this is how the world is. If that is true..

For the OP, same as I said above. If it is a fundmental rule then I guess I have to accept it. But the thing is, it looks like an invisible force acting on the charges because it is not a magentic force.

Biker said:
The problem in the first problem is that there is no actually B acting on the conductor. So there is no reason to use lorentz force. However, I may accept that lorentz force works in only some condition but the flux rule is more general because this is how the world is. If that is true..
Yes. That is true. Flux rule is the fundamental rule. Motional emf comes into picture only when the circuit is moving but there too, motional emf= dΦ/dt. It's just that it is easier to use the motional emf equation when the conductor is moving.
Biker said:
For the OP, same as I said above. If it is a fundmental rule then I guess I have to accept it. But the thing is, it looks like an invisible force acting on the charges because it is not a magentic force.
The invisible force is the electric force. An electric field is induced along the loop and that drives the current.
This induced electric field is such that
along the loopE⋅dl=dΦ/dt.

cnh1995 said:
Yes. That is true. Flux rule is the fundamental rule. Motional emf comes into picture only when the circuit is moving but there too, motional emf= dΦ/dt. It's just that it is easier to use the motional emf equation when the conductor is moving.

The invisible force is the electric force. An electric field is induced along the loop and that drives the current.
This induced electric field is such that
along the loopE⋅dl=dΦ/dt.
All right then thank you so much cnh1995,

There is no physical reasoning other than there is an electrical field induced in the loop (I already know about this), is there? but usually we say that this induced EF is just MF in case of motional emf but here it seems more of a mathematical equation rather than physical.

Thanks

Biker said:
There is no physical reasoning other than there is an electrical field induced in the loop (I already know about this), is there? but usually we say that this induced EF is just MF in case of motional emf but here it seems more of a mathematical equation rather than physical.
The the physical reason behind induced electric field in a stationary loop is explained using special relativity. You can read more about it later in web articles or standard physics books.

cnh1995 said:
The the physical reason behind induced electric field in a stationary loop is explained using special relativity. You can read more about it in web articles later.
Oh yeah I forgot, I read about it before not completely though. Got to focus on what I have first XD.

Thank you, I will mark this solved then.

## 1. What is Faraday's law and how does it relate to induced EMF in a circle?

Faraday's law states that the magnitude of an induced electromotive force (EMF) in a closed circuit is equal to the rate of change of the magnetic flux through the circuit. This means that when there is a change in the magnetic field passing through a conductive loop, an EMF will be created in that loop.

## 2. How is the direction of induced EMF determined in a circular loop?

The direction of the induced EMF in a circular loop is determined by the right-hand rule. If you point your thumb in the direction of the changing magnetic field, the direction of your curled fingers will indicate the direction of the induced current in the loop.

## 3. What factors affect the magnitude of induced EMF in a circular loop?

The magnitude of induced EMF in a circular loop is affected by the strength of the magnetic field, the area of the loop, and the rate of change of the magnetic field. The larger the magnetic field or the faster it changes, the greater the induced EMF will be.

## 4. Can induced EMF be negative in a circular loop?

Yes, induced EMF can be negative in a circular loop. This occurs when the direction of the changing magnetic field is opposite to the direction of the current in the loop, creating a decrease in the overall EMF.

## 5. How is Faraday's law used in practical applications?

Faraday's law is used in many practical applications such as generators, transformers, and induction cooktops. It is also the basis for many modern technologies, including electric motors and power plants.

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