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

AI Thread Summary
Induced EMF can occur in an open loop within a changing magnetic field, despite the absence of a closed circuit. Faraday's law is not directly applicable since there is no enclosed area, but the electric field generated by the changing magnetic field can be calculated using Maxwell's Equations. The voltage across the open loop can be determined by integrating the electric field along the loop. Although there is no continuous path for current flow, a capacitance exists at the ends of the wire, allowing for current to flow due to capacitive reactance. Understanding these principles is essential for accurately calculating induced EMF in such scenarios.
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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