• # question_answer A rectangular loop of sides 8 cm and 2 cm with a small cut is moving out of a region of uniform magnetic field of magnitude 0.3 T directed normal to the loop. What is the voltage developed across the cut, if velocity of loop is $1\text{ }cm{{s}^{-1}}$ in a direction normal to the (i) longer side (ii) shorter side of the loop For how long does the induced voltage last in each case?

Here, area, $A=8\times 2=16c{{m}^{2}}=16\times {{10}^{-4}}{{m}^{2}}$ $B=0.3.T,$ $v=1cm/s={{10}^{-2}}m/s$ Voltage developed, e = ? (i) When velocity is normal to longer side,             $l=8cm=8\times {{10}^{-2}}m$ $e=Blv=0.3\times 8\times {{10}^{-2}}\times {{10}^{-2}}=2.4\times {{10}^{-4}}V$ Induced emf lasts till the loop comes out of the magnetic field. Time,    $t=\frac{\text{Distance}\,\,\text{moved}}{\text{Velocity}}$             $t=\frac{2\times {{10}^{-2}}}{{{10}^{-2}}}$ $\Rightarrow$   t = 2s (ii) When velocity is normal to shorter side,             $l=2cm=2\times {{10}^{-2}}m$ $\therefore$ $e=Blv=0.3\times 2\times {{10}^{-2}}\times {{10}^{-2}}=0.6\times {{10}^{-4}}V$ The induced voltage lasts for time, $t=\frac{\text{Distance}\,\,\text{covered}}{\text{Velocity}}=\frac{8\times {{10}^{-2}}}{{{10}^{-2}}}=8\,\,s$
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