Charged Particle at rest in a Solenoid (conceptual question)

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SUMMARY

A charged particle at rest within a solenoid will not experience any force due to the magnetic field when the field is flipped instantaneously, as the initial velocity is zero (F = qv x B). The instantaneous change in the magnetic field does not produce a significant electromotive force (emf) affecting the particle's motion. Although Maxwell's equations indicate that a changing magnetic field generates an electric field, the practical implications of an instantaneous change suggest that the particle remains unaffected during this brief interval.

PREREQUISITES
  • Understanding of electromagnetic theory, specifically Maxwell's equations.
  • Familiarity with the Lorentz force law (F = qv x B).
  • Knowledge of solenoids and their magnetic field properties.
  • Concept of electromotive force (emf) in changing magnetic fields.
NEXT STEPS
  • Study the implications of Maxwell's equations on charged particles in magnetic fields.
  • Explore the concept of induced electric fields due to changing magnetic fields.
  • Investigate the behavior of charged particles in non-instantaneous magnetic field changes.
  • Learn about solenoid design and its applications in electromagnetic devices.
USEFUL FOR

Students of physics, particularly those studying electromagnetism, as well as educators and professionals seeking to deepen their understanding of charged particle dynamics in magnetic fields.

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Homework Statement


There is a solenoid with a magnetic field of a constant magnitude B. In this solenoid is a charged particle, initially at rest, at a certain distance r from the axis of the solenoid. After a certain amount of time, the magnetic field is instantaneously flipped in direction (magnitude remains the same). Will anything happen to the particle as a result of this flip, and if so, describe the trajectory of the particle.


Homework Equations


F = qv x B, where v is initially 0.


The Attempt at a Solution



Obviously, the particle starts at rest, and because of the fact that the particle has a velocity of zero, the magnetic field will not have any force on the particle. Normally, there would be an emf produced by the changing magnetic field of the solenoid as its magnetic field is being flipped, but in this particular case, since the change is instantaneous (or practically instantaneous), I think they want me to neglect the change in the magnetic field over time :/ This would mean that nothing would happen to the particle at all, right? But the way the problem is worded is unsettling to me, because it seems to imply that the particle actually would move, somehow.

I am kind of stuck on this problem, and any help would be greatly appreciated.
 
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I suspect the idea is to use that Maxwell law that says a changing magnetic field causes an electric field to circulate around it, proportional to the rate of change of the magnetic field. An infinite E field for an infinitesimal time?
 

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