How do you calculate induced EMF in an open loop with changing magnetic field?

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Discussion Overview

The discussion revolves around calculating the induced electromotive force (EMF) in an open loop subjected to a changing magnetic field. Participants explore the implications of induced EMF in the absence of a closed circuit, considering both theoretical and practical aspects of electromagnetic induction.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that while there may be an induced EMF in an open loop, calculating it using Faraday's law is problematic due to the lack of an enclosed area.
  • Another participant posits that if there is a voltage difference between the ends of the wire, it raises the question of whether current would flow, noting that without a complete path, current cannot flow.
  • A later reply emphasizes the need to determine the electric field resulting from the changing magnetic field by solving Maxwell's Equations, proposing to compute the voltage across the open loop through integration of the electric field along the loop.
  • Another participant introduces the concept of capacitance at the ends of the wire, suggesting that current could flow due to capacitive effects, referencing the relationship involving capacitive reactance.

Areas of Agreement / Disagreement

Participants express differing views on whether current can flow in the open loop and how to approach the calculation of induced EMF. There is no consensus on the correct method or the implications of the induced EMF in this scenario.

Contextual Notes

The discussion highlights limitations in applying Faraday's law to open loops and the assumptions regarding the presence of a path for current flow. The dependence on solving Maxwell's Equations and the role of capacitance are also noted as areas of complexity.

person123
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Let's say you have an open loop (like a section of a circle) in a changing magnetic field. I think there would be an induced EMF, but no current. What I can't figure out, though, is how to calculate the induced EMF. Using Faraday's law doesn't seem to help, as there's no enclosed area.
 
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Suppose there is EMF (voltage difference) between the ends. What do you think will happen? Would current flow through the wire?
 
scottdave said:
Suppose there is EMF (voltage difference) between the ends. What do you think will happen? Would current flow through the wire?
No, as there's no path for current to flow.
 
You would need to find the electric field (##\vec{E}##) due to changing magnetic field (by solving Maxwell's Equations), and then compute the voltage across the open loop ##C## by integrating the electric field along it ##V=-\int_C \vec{E}.\vec{\hat{l}} dl##
 
There is a capacitance due to the ends of the wire. Current will flow, due to Xc = 1/(omega*C)
 

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