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

[Sami Lakka]

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 = $$\omega \Phi cos(\omega t)$$

Where $$\Phi$$ is the peak magnetic flux and $$\omega$$ 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..

 

[cragar]

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