How Does a Moving Magnet Induce Voltage in a Rectangular Coil?

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SUMMARY

The discussion centers on the equation for voltage induced in a rectangular coil by a moving magnet, specifically V = L*dI/dt + RI = ωΦ cos(ωt). This equation incorporates the peak magnetic flux (Φ) and the angular frequency (ω) derived from the Halbach array's wavelength. The relationship between magnetic flux and induced voltage is established through the time derivative of magnetic flux, which is influenced by the angular frequency of the rotating cross-sectional area. The participants clarify that the induced voltage is a result of changes in magnetic flux due to the motion of the magnet.

PREREQUISITES
  • Understanding of electromagnetic induction principles
  • Familiarity with Halbach arrays and their applications
  • Knowledge of calculus, specifically derivatives
  • Basic concepts of alternating current (AC) voltage
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  • Study the derivation of Faraday's Law of Electromagnetic Induction
  • Explore the applications of Halbach arrays in magnetic levitation systems
  • Learn about the mathematical modeling of alternating current circuits
  • Investigate the effects of angular frequency on induced voltage in coils
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Sami Lakka
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I read interesting article regarding Halbach arrays and magnetic levitation (see www.lmco.cn/data/assets/9197.pdf[/URL]). In the article (see equation 1) the author states that the voltage generated by moving magnet over rectangular coil is

V= L*dI/dt + RI = [tex]\omega \Phi cos(\omega t)[/tex]

Where [tex] \Phi[/tex] is the peak magnetic flux and [tex] \omega[/tex] is the frequency defined by the wavelength of the Halbach array.

Where does the right side of this equation come from. Is it derivative from sin function containing the omega and phi? How is this equation formed? I'm puzzled..
 
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okay I've seen something similar . So magnetic flux is (area)B*cos(x)
and voltage is the time derivative of magnetic flux . let's say that we are rotating our cross sectional area with an angular frequency so now the flux is changing and we have a voltage . I will call my angular frequency Q so the flux is AB*cos(Qt)
so the time derivative of this will be voltage . This is what they do for alternating voltage.

B= field strength
 

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