Equilibrium, charge, and reaction question

[carrotcake10]

Homework Statement

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The figure shows an insulating ring and an infinite straight wire resting on the surface of an infinite plane. The wire is fixed in position, but the ring slides without friction on the surface of the plane. The ring is uniformly charged, with net positive charge Q. Initially, the wire carries a constant current I towards the top of the figure, and the ring is stationary. At time t=0, the current in the wire is reduced to I/2. Which of the following best describes the motion of the ring after the current is reduced?

1. The ring will spin clockwise and slide away from the wire.
2. The ring will spin clockwise and slide towards the wire.
3. The ring will spin clockwise and remain stationary.
4. The ring will not spin, but it will slide towards the wire.
5. The ring will spin counterclockwise and slide towards the wire.
6. The ring will spin counterclockwise and remain stationary.
7. The ring will not spin, but it will slide away from the wire.
8. The ring will spin clockwise and slide towards the top of the figure.
9. The ring will spin counterclockwise and slide towards the top of the figure.
10. The ring will not spin, but it will slide towards the bottom of the figure.
11. None of the above (please describe what does happen).

Hint: Think of the induced electric fields. If they can make current move, they can also apply a force or torque to a charge on an insulator.

The Attempt at a Solution

So obviously when the ring is stationary, the two objects are in static equilibrium, but I still don't know precisely how to answer this question. I think that if the current is halved, the electric field will be weaker.

What it comes down to is that I don't know the nature of two such objects given any conditions. Any links/explanations would be very helpful. My textbook, in my opinion, is fairly poor at conceptual explanations.

Thanks!

 

[anathema]

Thank you for your question. I can help provide some insight into the motion of the ring after the current is reduced.

First, let's consider the initial state where the current is I and the ring is stationary. In this state, the wire is producing a magnetic field which induces an electric field in the ring. This induced electric field creates a force on the charges in the ring, causing it to remain stationary.

Now, when the current is reduced to I/2, the induced electric field in the ring will also decrease. This means that the force on the charges in the ring will also decrease. As a result, the ring will experience a net force towards the wire. This force will cause the ring to slide towards the wire.

Additionally, the decrease in the induced electric field will also result in a decrease in the torque on the ring. This torque is what causes the ring to spin clockwise. With a weaker torque, the ring will either spin more slowly or not at all.

Therefore, the correct answer would be option 4: the ring will not spin, but it will slide towards the wire.

I hope this helps to clarify the motion of the ring in this scenario. If you have any further questions, please do not hesitate to ask.

 

[nlightner]

I would approach this question by first considering the concept of equilibrium. In this scenario, the wire and the ring are in static equilibrium when the ring is stationary. This means that the forces acting on the ring are balanced, resulting in no net force and therefore no acceleration.

Next, I would consider the concept of charge. The ring is uniformly charged with a positive charge Q. This means that it will experience a repulsive force from the positively charged wire due to the Coulomb's law.

Finally, I would consider the reaction to the change in current. When the current is halved, the induced electric fields will also be weaker. This means that the repulsive force between the wire and the ring will be weaker as well.

Based on these considerations, I would expect the ring to experience a net force towards the wire. This would result in the ring sliding towards the wire, but not spinning. Therefore, I would choose option 4 as the best description of the motion of the ring after the current is reduced.

However, it should also be noted that the motion of the ring will also depend on other factors such as the mass and charge of the ring, the distance between the wire and the ring, and the strength of the magnetic field produced by the current in the wire. These factors may result in a slightly different motion than what is expected based on the given information.