Confused about Polarity of Induced EMF (Lenz Law)

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Hello, Im currently working through Faraday's Law and im confused when my two textbooks dont explain how they set the polarity of [tex]V_{emf}[/tex], particularly when they say "the sign convention for [tex]V_{emf}[/tex] is arbitrary in that it depends on the assumed direction for dS". How is the polarity related to dS?

The formula im using is [tex]v_{emf} = - \int_c \vec{B}\cdot d\vec{S} = \oint_c \vec{E}\cdot d\vec{L}[/tex]

Here's a diagram that you can try explaining it from.

Thanks!
 

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  • #2
Doc Al
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For one thing, that equation is incorrect. http://hyperphysics.phy-astr.gsu.edu/Hbase/electric/farlaw.html" [Broken] states how the induced EMF relates to the rate of change of the magnetic flux ([itex]\Phi[/itex]):

[tex]{EMF} = - d\Phi/dt[/tex]

The polarity of the EMF (the meaning of the minus sign) is given by http://hyperphysics.phy-astr.gsu.edu/Hbase/electric/farlaw.html#c2".
 
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Oops i left out the time differential. Can anyone explain what my textbook is saying?
 
  • #4
Doc Al
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What they are trying to tell you is that the orientation of the surface determines the direction of the line integral. Imagine a circle (which we'll be finding the flux through) drawn on the x-y plane at z = 0 . If we arbitrarily choose +z as the direction of the surface element (dS) that means the line integral will go counter-clockwise when viewed from the +z axis looking down. And if we choose the opposite orientation, the line integral will go clockwise when viewed from +z.

So if we've chosen an orientation such that the line integral goes clockwise, a negative EMF means that the EMF is oriented counter-clockwise.

Make sense?
 
  • #5
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Doc Al. Lenz's Law in my text reads more like a hastily scribbled perscription than single law. First there's a given flux that yields the chirility of the EMF. Then an (implied) inducted current. Then the induced current is said to product a magnetic field that opposes the induced flux.
 
  • #6
Doc Al
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Doc Al. Lenz's Law in my text reads more like a hastily scribbled perscription than single law. First there's a given flux that yields the chirility of the EMF. Then an (implied) inducted current. Then the induced current is said to product a magnetic field that opposes the induced flux.
Lenz's law can be considered part of Faraday's law--the part that helps you determine the direction of the induced EMF (the negative sign in Faraday's law). It's a consequence of energy conservation. Not sure what you mean by calling it "hastily scribbled". :confused:
 
  • #7
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Lenz's law can be considered part of Faraday's law--the part that helps you determine the direction of the induced EMF (the negative sign in Faraday's law). It's a consequence of energy conservation. Not sure what you mean by calling it "hastily scribbled". :confused:
Well, perhaps "hasilt scribbled" is overly critical. But what I'm given are really three laws rather than one. If I break them down into my own numbering, Lenz1 determines the direction of EMF as you say.

The secone one (Lenz2) says that there could be a current as a result of the EMF, which seems to be a already obtained from Lorentz law.

Lenz3 says that an induced current generates an additional magnetic flux in opposition to the impressed flux. It's the result of two handedness operations, so I don't think it is really dependent upon Lenz1 anymore; the induced flux acts to impose the impressed flux no matter what handedness you give the coordinate system. Though my text later presents self inductance as a result of Lenz3, I'm skeptical that Lenz3 is an independent axiom that isn't inherent in Faraday's Law.
 

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