The figure shows a stationary conductor whose shape is similar to the letter e.

Question

The figure shows a stationary conductor whose shape is similar to the letter e. The radius of its circular portion is a = 45.0 cm. It is placed in a constant magnetic field of 0.90 T directed out of the page. A straight conducting rod, 45.0 cm long, is pivoted about point O and is being rotated with a constant angular speed of 1.30 rad/s. You will eventually be asked to find the EMF induced in the rotating bar.

tangentially counterclockwise (the rotation direction)tangentially clockwise    radially inwardradially outwardinto the pageout of the page

(b) Consider a small length element of the rotating bar having a length of 0.203 mm and being located at a distance of 15.000 cm from the stationary end of the rod at point O. What would be the contribution to the motional EMF integral from this small element of length in the rotating bar?
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(c) Consider another small length element (also of length 0.203 mm) within the rotating bar which is located at a distance of 30.000 cm from the point 0. What would be the contribution to the motional EMF integral from this second small element of length in the rotating bar?
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(d) Compute the motional EMF integral for this rotating bar, and thus determine the absolute value of the induced EMF in the rotating bar.
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Explanation / Answer

a)
? = -d?/dt

? = B ? A
d?/dt = B ? dA/dt (B is constant)

A = (1/2)?r

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