What is the EMF generated in the loop?

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SUMMARY

The discussion centers on calculating the electromotive force (emf) generated in a circular loop of wire with a diameter of 10 cm, positioned at a 30-degree angle to a uniform magnetic field of 0.50T. Despite the loop's rotation at a rate of 100 revolutions per minute, the emf is determined to be zero. This conclusion arises because the loop's normal remains fixed at the same angle, resulting in no change in magnetic flux through the loop, as per Faraday's law of electromagnetic induction.

PREREQUISITES
  • Understanding of Faraday's law of electromagnetic induction
  • Knowledge of magnetic flux and its calculation
  • Familiarity with the concept of electromotive force (emf)
  • Basic principles of circular motion and angular velocity
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  • Study the application of Faraday's law in different scenarios
  • Learn how to calculate magnetic flux through various shapes of loops
  • Explore the relationship between angular velocity and induced emf
  • Investigate the effects of varying magnetic field strength on induced emf
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Physics students, electrical engineers, and educators seeking to deepen their understanding of electromagnetic induction and its applications in real-world scenarios.

iggybaseball
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" A circular loop of wire 10 cm in diameter is placed with its normal making an angle of 30 degrees with the direction of a uniform 0.50T magnetic field. The loop is "wobbled" so that its normal rotates in a cone about the field direction at the constant rate of 100rev/min; the angle between the normal and the field direction (= 30 degrees) remains unchanged during the process. What emf appears in the loop?"

Alright I know that I am supposed to use the equation:
E(potential difference) = BDv
With B as the magnetic field, D as the area with a magnetic field that is not equal to 0 and v is the velocity. The back of the book says that the emf is zero. Is this because the loop is not being displaced ( it is wobbling in the same spot?) so it's velocity is zero?
 
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iggybaseball said:
Alright I know that I am supposed to use the equation:
E(potential difference) = BDv
That equation applies to a special case: That equation will calculate the motional EMF along a wire segment of length D that moves with speed v perpendicular to a magnetic field B.

Rather than struggle to apply this equation, consider the more general Faraday's law. (Look it up if you need to.) What's the flux through the loop? Does the flux change?
 

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