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

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The discussion centers on the equation for voltage induced by a moving magnet over a rectangular coil, expressed as V = L*dI/dt + RI = ωΦ cos(ωt). The participants explore the derivation of this equation, particularly how it relates to magnetic flux and angular frequency. They note that magnetic flux is calculated as the product of area and magnetic field strength, with voltage being the time derivative of this flux. The conversation highlights the connection between angular frequency and the changing magnetic flux that induces voltage, similar to principles used in alternating voltage systems. Understanding these relationships is crucial for applications involving Halbach arrays and magnetic levitation.
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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