What Happens to a Charged Ring When Current in a Nearby Wire is Halved?

[cpcolts]

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?

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

Force of Magnetic field= (mu-naught) (I^2)/(2*pi*r)

The Attempt at a Solution

OK so i feel like the answer is j. because when the current decreases the magnetic field will also decrease which will let the ring go and it slide down.
But I am not sure that the answer is right though.

Can someone please give me a reasoning towards the right answer?

 

[Jhero]

You are correct in thinking that the answer is j. When the current is reduced, the magnetic field created by the wire will also decrease. This decrease in magnetic field will result in a decrease in the force acting on the ring, causing it to move towards the bottom of the figure. This is due to the fact that the ring is positively charged and will experience a force in the opposite direction of the magnetic field. Therefore, the ring will slide towards the bottom of the figure as it is no longer held in place by the magnetic force. This is also known as the Lorentz force, which is given by the equation you mentioned in your post.

I hope this helps clarify the concept for you. If you have any further questions, please feel free to ask. Keep up the good work as a scientist!