Conceptual doubt - Rotating nonconducting ring

[Tanya Sharma]

Homework Statement

Consider a non conducting ring of radius r and mass m which has a total charge q distributed uniformly on it.The ring is rotated about its axis with an angular speed ω.
a)Find the equivalent electric current in the circuit.
b)Find the magnetic moment μ of the ring.

Homework Equations

The Attempt at a Solution

I know how to solve this problem .But I am finding it difficult to understand whether a rotating charge actually constitutes a current.If we consider any cross section of the ring then it looks like charge passes through it.But the cross section itself is moving .

I found a thread https://www.physicsforums.com/showthread.php?t=187946 somewhat related , especially post#5 by DaleSpam .But haven't been able to understand properly.

I would be grateful if someone could help me understand this.

 

[ehild]

Homework Statement

Consider a non conducting ring of radius r and mass m which has a total charge q distributed uniformly on it.The ring is rotated about its axis with an angular speed ω.
a)Find the equivalent electric current in the circuit.
b)Find the magnetic moment μ of the ring.

Homework Equations

The Attempt at a Solution

I know how to solve this problem .But I am finding it difficult to understand whether a rotating charge actually constitutes a current.If we consider any cross section of the ring then it looks like charge passes through it.But the cross section itself is moving .

With respect to the ring, the charges do not move. but outside it, in the rest frame of reference, you have a region where moving charge is present. The current density function in the rest frame of reference is zero everywhere except a stationary torus which surrounds the rotating ring. Across each cross section of that stationary torus there is charge flowing through.

ehild

 

[Tanya Sharma]

With respect to the ring, the charges do not move. but outside it, in the rest frame of reference, you have a region where moving charge is present. Across each cross section of that stationary torus there is charge flowing through.

ehild

I Agree . By rest frame I hope you mean lab frame.

The current density function in the rest frame of reference is zero everywhere except a stationary torus which surrounds the rotating ring.

Sorry ,I didn't understand this. What is current density function ? What is rest frame of reference here ?

My confusion is the definition of current - "Rate of flow of electric charge through a cross section of wire " .If we take any cross section of ring , there is no charge flowing through it .

Could you please help me understand what the mentor is conveying in https://www.physicsforums.com/showpost.php?p=1449312&postcount=5 ?

 

[ehild]

It is function of the position and means i=dI/dA, current flowing across an unit area, perpendicularly to it.

Do not take the cross section of the rotating ring, ring, but the torus which contains the ring. Charge flows across the cross sections of the torus.
If the charge moves with the same velocity and direction as the cross section, it will not cross the cross section. There is no current inside the moving ring, but the moving ring causes current in the world outside.

ehild

 

[Tanya Sharma]

1) Does that mean current is frame dependent?
2) In the definition of current, when we talk about cross sectional area, we mean a stationary cross section i.e
w.r.t ground .

Is it correct ?

 

[haruspex]

1) Does that mean current is frame dependent?
2) In the definition of current, when we talk about cross sectional area, we mean a stationary cross section i.e
w.r.t ground .

Is it correct ?

Yes, and yes.
It follows that the perception of a magnetic field is also frame dependent.

 

[Tanya Sharma]

Thank you very much.

 

[ehild]

1) Does that mean current is frame dependent?
2) In the definition of current, when we talk about cross sectional area, we mean a stationary cross section i.e
w.r.t ground .

Is it correct ?

Current is charge transfer in a medium. It depends on the speed of charge with respect to the medium. Imagine you push a charged box across the table. No charge transfer happens inside the block, but charge is transferred across the table.

ehild

 

[haruspex]

Current is charge transfer in a medium. It depends on the speed of charge with respect to the medium. Imagine you push a charged box across the table. No charge transfer happens inside the block, but charge is transferred across the table.

ehild

I don't think you're being quite consistent. If you define current as movement of charge wrt the medium then moving a charged object does not constitute a current. Surely it's the movement wrt the observer.

 

[ehild]

I don't think you're being quite consistent. If you define current as movement of charge wrt the medium then moving a charged object does not constitute a current. Surely it's the movement wrt the observer.

I did not mean current in general, but current in a medium.
When you speak about electric current you always specify the medium it flows. Current flows in a wire. Electrons fly from the cathode to the anode in a cathode-ray tube: it means current flowing in the cathode-ray tube. The current in a medium is the charge transferred across a cross section in unit time in that medium. The current in the wire or in the cathode-ray tube are the same either they are in rest in the lab or moving.
If you move a charged rod inside a tube, there is no current in the rod, but there is current in the tube, either you, the observer, are in rest with respect to the tube or moving with respect to it. In the OP, the medium where the current flows is the laboratory itself.

ehild

 

[haruspex]

I did not mean current in general, but current in a medium.
When you speak about electric current you always specify the medium it flows. Current flows in a wire. Electrons fly from the cathode to the anode in a cathode-ray tube: it means current flowing in the cathode-ray tube. The current in a medium is the charge transferred across a cross section in unit time in that medium. The current in the wire or in the cathode-ray tube are the same either they are in rest in the lab or moving.
If you move a charged rod inside a tube, there is no current in the rod, but there is current in the tube, either you, the observer, are in rest with respect to the tube or moving with respect to it. In the OP, the medium where the current flows is the laboratory itself.

ehild

OK, I suppose, but it doesn't seem a very useful way to think about it. If I have a current flowing in a wire, and next to that I have a magnet moving with the same velocity as the electrons, the magnet will not sense the current. So what benefit is there in thinking of the current as being wrt the medium rather than wrt the observer?

 

[ehild]

OK, I suppose, but it doesn't seem a very useful way to think about it. If I have a current flowing in a wire, and next to that I have a magnet moving with the same velocity as the electrons, the magnet will not sense the current. So what benefit is there in thinking of the current as being wrt the medium rather than wrt the observer?

Imagine you connect a lamp to the supply with a two-wire cable. (The two wires are very close together in the cable)
Certainly, there is current flowing in the wires, as the lamp lights. Does any charge flowing across any cross section in the room ? Has it sense to say that 1 A current flows in the room?

In your problem, the current induces magnetic field around the wire in the lab frame of reference. It will certainly act to the moving magnet. I am not sure if that interaction ceases when the magnet moves with the same velocity as the charge carriers inside the wire. But I know next to nothing about electrodynamics of moving bodies.
ehild

 

[rude man]

Getting back to the OP's original post:
Think of 2 situations:
1. A stationary ring carrying current: the observer sees charges buzzing around the ring.
2. A rotating ring with stationary charges within the ring: the observer sees charges buzzing around the ring.

So to the observer the two situations are indistinguishable from each other electrically. Kind of like Einstein's elevator Gedankenexperiment with gravity & acceleration being indistinguishable.