A) \[\pi rB\left( \frac{dr}{dt} \right)\]
B) \[2\pi rB\left( \frac{dr}{dt} \right)\]
C) \[\pi {{r}^{2}}\left( \frac{dr}{dt} \right)\]
D) \[{{\left( \frac{\pi {{r}^{2}}}{2} \right)}^{2}}B\left( \frac{dr}{dt} \right)\]
Correct Answer: B
Solution :
Induced emf is given by \[e=-\frac{d\phi }{dt}\] If the radius of loop is r at a time t, then the instantaneous magnetic flux is given by \[\phi =\pi {{r}^{2}}B\] \[\therefore \] \[e=-\frac{d}{dt}(\pi {{r}^{2}}B)\] \[e=-\pi B\left( \frac{2r\,\,dr}{dt} \right)\] \[e=-2\pi Br\frac{dr}{dt}\] Numerically, \[e=2\pi Br\left( \frac{dr}{dt} \right)\]
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