Why does induced current in loop vary twice with rotation of coil?

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SUMMARY

The induced current in a rotating square loop of wire varies twice with the frequency of rotation due to the magnetic flux changes experienced by the loop. As the loop rotates with frequency ω in a magnetic field described by B = B₀sin(ωt), the electromotive force (emf) induced is proportional to the rate of change of magnetic flux. This results in two cycles of current per complete rotation of the coil. The expression for the induced current can be derived using Maxwell's equations and Ohm's law.

PREREQUISITES
  • Understanding of electromagnetic induction principles
  • Familiarity with Maxwell's equations
  • Knowledge of Ohm's law
  • Basic concepts of magnetic flux
NEXT STEPS
  • Study the derivation of induced emf from Maxwell's equations
  • Explore the relationship between magnetic flux and induced current
  • Learn about the effects of coil rotation speed on induced current
  • Investigate applications of induced current in electromagnetic devices
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Physics students, electrical engineers, and anyone interested in the principles of electromagnetic induction and its applications in rotating systems.

trelek2
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A square loop of wire of side a is rotating with frequency \omega in a magnetic field. I understand that at time t, a magnetic field B=B_{0}sin\omega t passes through the loop. But why does the current induced in the loop vary twice with the frequency of rotation? What is the expression of the current induced?
 
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trelek2 said:
A square loop of wire of side a is rotating with frequency \omega in a magnetic field. I understand that at time t, a magnetic field B=B_{0}sin\omega t passes through the loop. But why does the current induced in the loop vary twice with the frequency of rotation? What is the expression of the current induced?

The emf induced around the contour of the coil is proportional to the rate at which the magnetic flux through the coil varies in time. This variation undergoes two min/max/min cycles per rotation of the coil. Hence current in the coil pulses twice per revolution. The current induced can be calculated from Maxwell's equation for the curl of E, plus Ohm's law.
 

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