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An elasticized conducting band is around a spherical ballon . Its plane through the center of the balloon. A uniform nmagnetic field of magnitude `0.04T` is directed perpendicular to the plane of the band. Air is let out of the balloon at `100 cm^(3) s^(-1)` at an instant when the radius of the balloon is `10 cm`. The induced emf in the band is A. (a) `15mu v`B. (b) `25mu v`C. ( c) `10mu v`D. (d) `20mu v` |
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Answer» Correct Answer - D (d) Volume of the balloon at any instant, when rdius is `r`, `V = (4)/(3)pir^(3)` Time rate of change of volume, `(dV)/(dt) = 4pir^(2)(dr)/(dt)` Time rate of change of radius of balloon, `(dr)/(dt) = (1)/(4pir^(2))(dV)/(dt)` Flux through rubber band at the given instant, `phi = B(pir^(2))` `Induced emf = -(dphi)/(dt) = -(d)/(dt)(Bpir^(2)) = -2pirB(dr)/(dt)` `= -2pirB.((1)/(4pir^(2))(dV)/(dt)) = -(B)/(2r)(dV)/(dt)` As volume of the balloon is decreasing, `(dV)/(dt)` is negative. `E_(induced) = -((0.04))/(2 xx 10 xx 10^(-2)) xx (-100 xx 10^(-6)) = 20mu V` |
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