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A line charge `lambda` per unit length is pasted uniformly on to the wire of a wheel of mass `m` and radius `R`. The wheel has light non-conducting spokes and is free to rotate about a vertical axis as shown in `Fig. 3.166`. A uniform magnetic field extends over a radial rigion of radius `r` given by `B = -B_(0)hat(k)(r le a, alt R) = 0` (otherwise). What is the angular velocity of the wheel this field is suddenly switched off? A. (a) `(-2B_(0)pia^(2)r)/(mR)hat(k)`B. (b) `(-2B_(0)pia^(2)r)/(3mR)hat(k)`C. ( c) `(B_(0)pia^(2)lambda)/(mR)hat(k)`D. ( d) `(-B_(0)pia^(2)lambda)/(mR)hat(k)` |
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Answer» Correct Answer - D (d) Induced `E = (a^(2))/(2R)(dB)/(dt)` `Iomega = int tau dt` `rarr` `mR^(2)omega = int qERdt = int(qa^(2))/(2R)(dB)/(dt)Rdt = (lambda2piR)/(2R)a^(2)RintdB` `rarr` `omega = (B_(0)pia^(2)lambda)/(mR)` `rarr vec(omega) = -(B_(0)pia^(2)lambda)/(mR)hat(k)` (because clockwise sense) |
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