Induced EMF in a rotating ring

In summary, the phenomenon of induced electromotive force (EMF) in a rotating ring occurs when a conductive ring is rotated in a magnetic field. As the ring moves through the magnetic field, a change in magnetic flux occurs, which induces an EMF according to Faraday's law of electromagnetic induction. This induced EMF can generate a current if the circuit is closed, illustrating the principles of electromagnetic induction and the relationship between motion, magnetic fields, and electric currents. The study of this effect has applications in various technologies, including electric generators and motors.
  • #1
gochaka
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[Thread moved from the technical forums to the schoolwork forums]

Let's suppose we have a ring with radias R and radius of the cross section r. We start rotating with an angular velosity w. We will there be an induced EMF in the ring and how can i find it's value?
 
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  • #2
Welcome to PF.

gochaka said:
Let's suppose we have a ring with radias R and radius of the cross section r. We start rotating with an angular velosity w. We will there be an induced EMF in the ring and how can i find it's value?
What material is the ring made from?
About what axis does the ring rotate?
Is there a magnetic field?
What orientation field?
 
  • #3
Hello gochaka. To answer your question straight up, that would be a no. Questions about this concept are posted repeatedly on PF, so you are not alone. To get an induced voltage, you must have a changing magnetic flux through the cross- sectional area.
 
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  • #4
gochaka said:
Let's suppose we have a ring with radias R and radius of the cross section r. We start rotating with an angular velosity w. We will there be an induced EMF in the ring and how can i find it's value?
Whelp, if there is a magnet nearby, what do you think? What are the Relevant Equations for this type of calculation? Is this question for schoolwork?
 
  • #5
There isn't an external magnetic field. The material of which there ring is made of the doesn't matter. You only know it's resistance . Also there surely is an induced EMF since this question was used in a very prestigious competition four years ago.
 
  • #6
Maybe you should post the question verbatim.
 
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  • #7
gochaka said:
There isn't an external magnetic field. The material of which there ring is made of the doesn't matter. You only know it's resistance . Also there surely is an induced EMF since this question was used in a very prestigious competition four years ago.
That's hard to believe that there isn't an external field. You can't simply spin something and there magically be a voltage.
 
  • #8
Thread moved from the technical forums to the schoolwork forums
Problem 5. A copper ring of cross-section S = 1 mm2 and radius r = 5 cm starts rotating
around its axis with a constant angular acceleration α = 1000 rad/s2
. Find the magnetic field
B at the centre of the ring. The resistivity of copper is ρ = 1.68 × 10−8 Ωm.
Hint: You may want to work in the reference frame of the rotating ring. What is the force that
gives rise to an EMF in the ring?

That's the original question used in the olympiad.
 
  • #9
First, Olympiad problems are not B-level.
Second, you omitted a lot of relevant information in the OP.
Third, you miswrote the problem - you wrote angular velocity when it fact there is an angular acceleration.

So, how far did you get?
 
  • #10
I don't even know where to start from
 
  • #11
gochaka said:
Problem 5. A copper ring of cross-section S = 1 mm2 and radius r = 5 cm starts rotating
around its axis with a constant angular acceleration α = 1000 rad/s2
. Find the magnetic field
B at the centre of the ring. The resistivity of copper is ρ = 1.68 × 10−8 Ωm.
Hint: You may want to work in the reference frame of the rotating ring. What is the force that
gives rise to an EMF in the ring?

That's the original question used in the olympiad.

You are leaving out the part about there being a B-field in the region of the ring. As mentioned already, without a changing magnetic flux in the ring, there will be no EMF induced.

And since this is a schoolwork-type question, I'll move the thread to the schoolwork forums.
 
  • #12
gochaka said:
I don't even know where to start from
That is not acceptable in a schoolwork-type thread. You have to show your efforts before we can offer tutorial help.

** Where is the B-field coming from? There has to be one somewhere in the problem statement or diagram.

** What are the relevant equations for induced EMF for a changing flux through a conducting ring?
 
  • #13
I think the B-field is internally generated. There is something in the actual question (but not the OP) that hints at it. But I don't want to mention it until the OP puts in at least a smidgen of work.
 
  • #15
Zero-effort poster @gochaka has not been back to this thread for several days, so I will tie it off. @gochaka -- if you do return and are willing to show some effort on this problem, please send me a Personal Message (PM) by clicking twice on my avatar and "Start a Conversation". If you are willing to show some effort I can reopen this thread.

Thanks all for trying to help the OP.
 
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FAQ: Induced EMF in a rotating ring

What is induced EMF in a rotating ring?

Induced EMF (Electromotive Force) in a rotating ring refers to the voltage generated in a conductive ring when it is rotated in a magnetic field. This phenomenon is a result of electromagnetic induction, where a change in magnetic flux through the ring induces an electric current according to Faraday's Law of Induction.

How is the induced EMF calculated in a rotating ring?

The induced EMF (\( \mathcal{E} \)) in a rotating ring can be calculated using Faraday's Law, which states that the induced EMF is equal to the negative rate of change of magnetic flux (\( \Phi \)) through the ring. Mathematically, it can be expressed as \( \mathcal{E} = -\frac{d\Phi}{dt} \). For a rotating ring in a uniform magnetic field, the expression can be further simplified to \( \mathcal{E} = B \cdot A \cdot \omega \), where \( B \) is the magnetic field strength, \( A \) is the area of the ring, and \( \omega \) is the angular velocity of the rotation.

What factors affect the magnitude of the induced EMF in a rotating ring?

The magnitude of the induced EMF in a rotating ring is affected by several factors, including the strength of the magnetic field (\( B \)), the area of the ring (\( A \)), the angular velocity of rotation (\( \omega \)), and the orientation of the ring relative to the magnetic field lines. Increasing any of these factors will result in a higher induced EMF.

Does the direction of rotation affect the induced EMF?

Yes, the direction of rotation does affect the induced EMF. According to Lenz's Law, the direction of the induced current will oppose the change in magnetic flux that produced it. Therefore, if the direction of rotation is reversed, the direction of the induced EMF and the resulting current will also reverse.

Can induced EMF in a rotating ring be used for practical applications?

Yes, induced EMF in a rotating ring has practical applications, particularly in the generation of electricity. This principle is utilized in devices such as generators, where mechanical energy is converted into electrical energy. Additionally, it can be used in various sensors and electromagnetic devices where the detection of motion or rotation is required.

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