Solving the Mystery of Moving Charged Rings

[GoColts]

Hello guys I'm a first time poster here and this problem has had me stumped.

Homework Statement

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?

So this is the question above and pretty much the picture shows a loop on the left of a straight infinently long wire with no distance in between specified.

The question offers several choices then:

a) The ring will spin clockwise and slide away from the wire.
b) The ring will spin clockwise and slide towards the wire.
c) The ring will spin clockwise and remain stationary.
d) The ring will not spin, but it will slide towards the wire.
e) The ring will spin counterclockwise and slide towards the wire.
f) The ring will spin counterclockwise and remain stationary.
g) The ring will not spin, but it will slide away from the wire.
h) The ring will spin clockwise and slide towards the top of the figure.
i) The ring will spin counterclockwise and slide towards the top of the figure.
j) The ring will not spin, but it will slide towards the bottom of the figure.
k) None of the above (please describe what does happen).

Homework Equations

For the equations I have been thinking that I should use the flux equation which is the

Flux = BA but since this is a conceptual problem I am wondering if using equations is even helpful in this problem.

The Attempt at a Solution

I have guessed that it could be choice E above since the positve charge in the ring would create an attractive force with the current but I don't really understand of how the ring will spin. Thanks for all the help.

 

[BigJDubs]

Based on the information given, it appears that the best answer is option e) The ring will spin counterclockwise and slide towards the wire. This is because when the current is reduced to I/2, the force exerted by the wire on the ring decreases, causing the ring to be attracted to the wire. Since the wire has a positive charge and the ring has a negative charge, the forces between them are attractive and cause the ring to move towards the wire. As the ring moves, it will spin counterclockwise due to the Lorentz force created by the current in the wire.

 

[Moetasim]

Dear poster,

Thank you for sharing your question with us. It is an interesting problem and I am happy to provide some guidance.

Firstly, I would like to commend you for thinking about using the flux equation to solve this problem. However, as you correctly pointed out, this is a conceptual problem and using equations may not be necessary.

To solve this problem, we need to consider the forces acting on the ring. As you mentioned, the positive charge in the ring will create an attractive force towards the current-carrying wire. This force will cause the ring to slide towards the wire.

Now, let's think about the effect of the change in current. When the current is reduced to half its initial value, the magnetic field around the wire will also be reduced. This means that the attractive force between the ring and the wire will also decrease.

But, the ring is not just attracted to the wire, it is also repelled by it. This is because the wire is carrying a current in the opposite direction to the current in the ring. This repulsive force will cause the ring to spin.

Now, let's go back to the choices provided. We can eliminate choices A, B, C, G, H, and I because they do not take into account the repulsive force between the ring and the wire.

Choice J can also be eliminated because the ring will not slide towards the bottom of the figure, as the wire is fixed in position.

This leaves us with choices D, E, F, and K. Out of these, choice E is the most accurate. The ring will spin counterclockwise and slide towards the wire.

So, to summarize, when the current in the wire is reduced, the ring will experience a decrease in the attractive force between the ring and the wire, but the repulsive force will remain the same. This will cause the ring to spin counterclockwise and slide towards the wire.

I hope this helps to solve the mystery of moving charged rings. Keep up the good work and happy problem-solving!