Potential difference of a ring rolling in magnetic field

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SUMMARY

The discussion centers on the potential difference (p.d.) between points A and O in a ring rolling in a magnetic field. Participants clarify that while the magnetic field through the ring's cross-sectional area remains constant, a p.d. can still exist due to the lateral motion of the ring through the magnetic field. The induced electromotive force (emf) is derived from the motion of charge carriers within the ring, specifically using the integral $$\int_0^{\pi} (\vec{B}\times\vec{v})\cdot \vec{dl}$$ to calculate the emf between points A and O. The conversation emphasizes that the ring behaves as a cell with a positive terminal at A and a negative terminal at O, but does not allow current to flow due to the absence of a complete circuit.

PREREQUISITES
  • Understanding of Faraday's Law of Induction
  • Familiarity with electromotive force (emf) concepts
  • Knowledge of magnetic fields and their interaction with moving conductors
  • Basic calculus for evaluating integrals
NEXT STEPS
  • Study the derivation of Faraday's Law of Induction in detail
  • Learn about the calculation of motional emf using integrals
  • Explore the effects of magnetic fields on rotating and translating conductors
  • Investigate the implications of induced current in circuits with varying magnetic fields
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Physics students, electrical engineers, and anyone interested in electromagnetic theory and applications involving moving conductors in magnetic fields.

  • #31
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  • #32
A couple posts were removed by the request of the poster (along with a reply to the posts), and the thread is re-opened for now. Thanks everybody for your patience.
 
  • #33
I deleted my posts (##25 ff.) since my argument was not really relevant. @ergospherical 's explanation is certainly correct but his statement "The assumption of a constant and uniform magnetic field means there is a well defined electric potential field" is IMO not obvious to an introductory physics student. Interestingly, his E field is the irrotational field formed by charge buildup while ## \bf v \times \bf B ## is the induced, and therefore non-conservative component.

Note too that if the observer were to move with the ring then the latter term would be absent, implying in its place a second E field to null the irrotational one. The physics in either case is obviously the same. If this is not accepted then we need to throw out the well-worn dictum that "the net E field in a conductor is zero".
 
  • #34
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  • #35
Sigh, after multiple thread derailments, this thread will remain closed.
 
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