A rectangular wire 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 emf developed across the cut if the velocity of the loop is `1 "cm s"^(-1)` in a direction normal to the (a) longer side, (b) shorter side of the loop ? For how long does the induced voltage last in each case ?

Explanation

As shown in figure (2),
`V_(pq)=V_(pt)+V_(ts)+V_(sr)+V_(rq)`
`therefore V_(pq)=0+0+epsilon+0` ( `because` For side pt,B=0 and for sides ts and rq , `vecv||vecl`)
=Bvl
`=(0.3)(1xx10^(-2))(8xx10^(-2))`
`therefore V_(pq)=0.24xx10^(-3)` V
`=2.4xx10^(-4)` V

As shown in figure (4),
`V_(pq)=V_(pt)+V_(ts)+V_(sr)+V_(rq)`
`=0+epsilon.+0+0` ( `because` For side rq , B=0 and for sides pt and sr , `vecv||vecb`)
=Bvb
`=(0.3)(1xx10^(-2))(2xx10^(-2))`
`=0.06xx10^(-3) V`=0.06 mV
Here emf induced in longer side will last for time `t_1` in which shorter side comes out of magnetic field . Hence, `v=b/t_1`
`therefore t_1=b/v=(2xx10^(-2))/(1xx10^(-2))=2s`
Similarly emf induced in shorter side will last for time `t_2` in which longer side comes out of magnetic field. Hence, `v=l/t_2`
`therefore t_2=l/v = (8xx10^(-2))/(1xx10^(-2))`=8s