Current vs. Time: Mathematical Expression for Hippolyte Pixii's Dynamo

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SUMMARY

The current generated by Hippolyte Pixii's dynamo can be mathematically expressed as a cosine function, specifically I(t) = (2/π)^(0.5) * cos(ω0 * t), where I(t) represents the current at time t and ω0 is the angular frequency of the rotating magnet. This expression assumes that the maximum current occurs when the magnet's pole is aligned with the coil. The discussion emphasizes the importance of understanding the relationship between current and time in the context of alternating current generators.

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Consider a simple alternating current generator such as Hippolyte Pixii's dynamo. The current generated by such dynamo can be described as simple oscillating cosine signal. Assuming for simplicity that the max current generated each time a pole of Pixii's magnet passed the coil is (2/pi)0.5 amperes and that the magnet rotate with a characteristic angular frequency ω0.

Write the mathmatical expression for the time-domain signal (current vs. time) from such AC generator. For simplicity, assume that the magnet was already spinning at the beginning of the observation and the magnet's poled happened to be just below the coils at time zero.

I am not really sure how to start, I just need know that I need something relate current with time and equation should have cosine.
Thanks for any help
 
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