A conducting bar of length l rotates with a constant angular speed w about a piv

Question

A conducting bar of length l rotates with a constant angular speed w about a pivot at one end. A uniform magnetic field B is directed perpendicular to the plane of rotation as shown in Figure 23.12. Find the motional emf induced between the ends of the bar. SOLUTION Conceptualize The rotating bar is different in nature from the sliding bar in Active Figure 23.11. Consider a small segment of the bar, however. It is a short length of conductor moving in a magnetic field and has an emf generated in it like the sliding bar. By thinking of each small segment as a source of emf, we see that all segments are in

Explanation / Answer

that 1/2 comes from the integration

since motional emf V = B * v * l

if we take a small piece of rod dr so

dV = B * v * dr

in case of rotational motion

v = ?r

so,

dV = B * ? * r * dr

on integrating the above equation from 0 to L we get

V = (1/2)B?L2

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