Magnetic flux through a rotating bar

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SUMMARY

The discussion centers on the concept of magnetic flux through a rotating bar, specifically addressing the induced electromotive force (emf) in a uniform magnetic field as described in Serway and Jewett's physics textbook. The key takeaway is that while the magnetic field (B) and the area may appear constant, the changing angle of the bar as it rotates alters the effective area through which the magnetic field lines pass, leading to a variation in magnetic flux. This results in an induced emf that can be calculated using the formula dEMF = Bvdr, where v is the velocity of the bar and dr is the differential change in radius.

PREREQUISITES
  • Understanding of magnetic flux and its mathematical definition.
  • Familiarity with Faraday's law of electromagnetic induction.
  • Knowledge of the relationship between velocity, length, and induced emf in magnetic fields.
  • Basic concepts of rotational motion and angular displacement.
NEXT STEPS
  • Study the derivation of Faraday's law in the context of rotating systems.
  • Explore the implications of varying magnetic flux in practical applications, such as electric generators.
  • Learn about the effects of angular velocity on induced emf in rotating conductors.
  • Investigate the relationship between magnetic field strength and induced current in different configurations.
USEFUL FOR

Students of physics, educators teaching electromagnetism, and engineers working with electromagnetic systems will benefit from this discussion.

Baptiste Debes
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Hello everyone,
My question is between theorie and practical (so I'm still wondering if it's the right place). I'm reading Serway and Jewett. There's an example about the magnetic flux through a rotating bar and so and induced emf. I understand this emf will be equal to the the opposite of the variation of magnetic flux with respect to the time. But here, as you may see in the picture, B is uniform. (Hoping I can post this kind of picture, I'll delete it straightaway if not)
JdsCX9g.png

So why is the flux changing ? The area (assuming there is one ?), angle and B field are constant. They're actually using a result coming from a previous example : the sliding bar on two rails with a resistance R between and immerged in a uniform magnetic field. This result is that EMF = -Blv (with l the length of the bar and v its speed). I understood this. But I don't get it when they're using it for the rotating bar saying dEMF = Bvdr.

Many thanks,

Baptiste Debes
 
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Baptiste Debes said:
So why is the flux changing ?
The area "swept by" the bar is changing.
 
Ok, I understand, but this area is the same and B is uniform. When you take definition of magnetic flux and than its variation with time I don't see mention of this kind of change.

Thank you for the time you're giving to me
 

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