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A rotating paddle wheel of rectangle cross section, of height H, and of length L is...

A rotating paddle wheel of rectangle cross section, of height H, and of length L is placed at the origin with the center axis of the paddle wheel along the z axis. It is rotating at an angular speed of ω around the z axis, Assume that the paddle wheel is placed into a uniform E~ field. Find the flux Φ through the surface as a function of time. Find dΦ dt .

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