Potential difference of a ring rolling in magnetic field

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The discussion centers on the potential difference (p.d.) between points A and O on a ring rolling in a magnetic field. Participants debate whether a change in magnetic flux is necessary to explain the p.d., with some arguing that since the magnetic field is constant, no current should flow. However, it is clarified that the lateral motion of the ring through the magnetic field generates a non-zero motional EMF, despite the overall EMF for the entire ring being zero. The conversation also touches on the mathematical derivation of EMF using integrals and the effects of the ring's motion. Ultimately, the participants conclude that the p.d. arises from the combination of translational and rotational motion of the ring.
  • #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".
 
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  • #35
Sigh, after multiple thread derailments, this thread will remain closed.
 
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