Motion of Ring After Current Reduction in Hoop, Line and Stinker

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SUMMARY

The discussion centers on the motion of a uniformly charged insulating ring in response to a reduction in current through an infinite straight wire. When the current is halved from I to I/2, the magnetic field around the wire decreases, leading to an induced current in the ring due to Lenz's law. The consensus is that the ring will spin clockwise and slide towards the bottom of the figure, confirming option j as the correct answer. This motion is a direct consequence of the ring's response to the changing magnetic flux.

PREREQUISITES
  • Understanding of Lenz's Law and its implications on induced currents.
  • Familiarity with magnetic fields generated by current-carrying wires.
  • Knowledge of the motion of charged objects in magnetic fields.
  • Basic principles of electromagnetism and magnetic flux.
NEXT STEPS
  • Study the principles of Lenz's Law in greater detail.
  • Explore the effects of changing magnetic fields on charged conductors.
  • Investigate the dynamics of charged rings in electromagnetic fields.
  • Learn about the applications of induced currents in practical scenarios.
USEFUL FOR

Students of electromagnetism, physics educators, and engineers interested in the behavior of charged objects in magnetic fields will benefit from this discussion.

cpcolts
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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?

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).



my 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?
 
Last edited:
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Without a figure as reference, I can only speak in generalities. I assume that the ring is free to spin and/or translate in response to the changing current in the wire. This is a Lenz's law problem. Since the magnetic flux through the ring will decrease as a result of the reduced current, the induced current in the ring will flow so that forces and torques will be generated to oppose this proposed change. The ring will spin and move in whatever fashion will increase the decreasing magnetic flux through it.
 

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