Does a rotating ring of uniform charge constitute a current?

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Discussion Overview

The discussion revolves around whether a rotating ring of uniform charge constitutes an electrical current. Participants explore the implications of charge movement in different frames of reference, the definitions of current, and the resulting magnetic fields. The scope includes theoretical considerations and conceptual clarifications related to electromagnetism.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • Some participants argue that a rotating charged ring produces a current because charge carriers move through a "window" in the ring, suggesting a flow of charge.
  • Others contend that considering an infinitesimal segment of the ring shows that dQ/dt = 0 at all times, leading to the conclusion that there is no current.
  • One participant references historical experiments by Roentgen and Eichelwald to support the idea that a rotating charged ring constitutes a current.
  • Another participant asserts that while the current density flux through any closed surface on the ring is zero, this does not negate the existence of a current, as charges cross open surfaces.
  • A different viewpoint suggests that current does not necessarily require a change in total charge, citing examples like induced current in a circular loop with a magnet.
  • Some participants mention that the rotating charged ring generates a magnetic field, linking it to the concept of convection current.
  • One participant draws an analogy to a cathode ray tube to illustrate the concept of convection current versus conduction current.

Areas of Agreement / Disagreement

Participants express differing views on whether the rotating ring constitutes a current, with some asserting it does and others arguing against it. The discussion remains unresolved, with multiple competing perspectives presented.

Contextual Notes

Participants highlight the complexity of defining current in relation to moving surfaces and charge density, indicating that assumptions about charge distribution and frame of reference may influence conclusions.

Zorodius
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If I have a charged insulating hula-hoop with the property that every point on the ring has exactly the same charge per volume as every other point on the ring, and I spin it around its axis, does that produce a current?

If I consider a "window" cutting through some part of the ring, I will see charge carriers moving through that window, so I'd think there is a current.

But if I consider any segment of the ring of infinitesimal length, dQ/dt = 0 at all times, so I'd think there is not a current.

Which is right?
 
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Roentgen and also Eichelwald did this experiment in the 1800's. Ref. Richard Becker "Electromagnetic Fields and Interactions"
 
It is a current and will result in a magnetic field. Current is the flow of charge in space. In the frame of the ring there is no current.
 
ansrivas said:
It is a current and will result in a magnetic field. Current is the flow of charge in space.
Well, why? The current density flux through any closed surface on the ring is always zero, and that should be equal to the current.

From the perspective of Ampere's law, I would think there would be a current, because charges will cross an open surface that cuts the ring. But from the perspective of the current density, I would think there is not a current. Why is one answer wrong?
 
Zorodius said:
Well, why? The current density flux through any closed surface on the ring is always zero, and that should be equal to the current.
No, in this case a closed surface on the ring is moving, you cannot use a moving surface to determine a current. Let's consider an absurd example to demonstrate the point. Let's say that you have a wire with only positive charge carriers moving at exactly 1 m/s. This is clearly a current. Now let's make a surface that also moves at 1 m/s, no net flux through it. According to your logic that would eliminate the current. That is why you cannot use a moving surface to determine current.

-Regards
Dale
 
Zorodius said:
But if I consider any segment of the ring of infinitesimal length, dQ/dt = 0 at all times, so I'd think there is not a current.
I don't think a current is necessarily given by dQ/dt. Consider the case of a circular loop with a current induced by a magnet being drawn through its center. The system is symmetric, so charge should be constant around the loop.

Current does not need a change in total charge to take place. Change in charge or charge density will lead to a divergence, source or sink, of current. But current can flow and even increase or decrease without charge building up.

Charge and current are sometimes separate in classical electro magnetics.

To answer the original question, not only are charges moving in the circular system, they are accelerating. There is a current, and a magnetic field will be generated. In fact, the system you describe is perhaps akin to charged plasma in a tokamak.
 
Zorodius said:
If I have a charged insulating hula-hoop with the property that every point on the ring has exactly the same charge per volume as every other point on the ring, and I spin it around its axis, does that produce a current?

If I consider a "window" cutting through some part of the ring, I will see charge carriers moving through that window, so I'd think there is a current.

But if I consider any segment of the ring of infinitesimal length, dQ/dt = 0 at all times, so I'd think there is not a current.

Which is right?

You can sense (or measure) the magnetic field by holding a compass near your rotating, charged hoop. But, if you mount the compass on the moving hoop, the dipoles of the compass needle will be moving and generate an electric field that interacts with the electric field of the hoop. This interaction will cancel any torque on the compass.
 
The answer is yes, a rotating charged ring does constitute an electrical current in the laboratory (nonrotating) frame -- this kind of electric current is called a convection current --anytime you have bare charges moving relative to the observer (as in this case) there is an electrical current called a convection current and i does produce a magnetic field.
 
jimmd said:
The answer is yes, a rotating charged ring does constitute an electrical current in the laboratory (nonrotating) frame -- this kind of electric current is called a convection current --anytime you have bare charges moving relative to the observer (as in this case) there is an electrical current called a convection current and i does produce a magnetic field.

Another example of a convection current is the electron beam in a cathode ray tube.

By the way, the typical kind of electric current that you have in an electical wire in which electrons move through the copper conductor is called a conduction current.
 

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