A rectangular wire loop of sides 8 cm and 2 cm with a small cut is moving out of 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

Given length of the loop `l= 8 cm= 8 xx 10^(-2)m`.
Width of the loop `b= 2cm= 2 xx 10^(-2)m.`
Velocity of the loop `=1 cm/s =0.01m/s.`
Magnitude of magnetic field (B) =0.3T
(a) When velocity is normal to the longer side `(l=8 cm=8xx 10^(-2)m)`
In this case, motinal emf `e=B//upsilon =0.3xx8xx10^(-2)xx0.01=2.4xx10^(-4)V`
`"Time"=("Distance")/("Velocity")=("Shorter side(width)")/("Velocity")`
`t=(2xx10^(-2))/(0.01)=2s`
(b) When velocity is normal to the shorter side `(l=2cm =2 xx 10^(-2)m)`
In this case, the developed emf
`e=B//upsilon =0.3xx2xx10^(-2)xx0.01`
`0.6xx10^(-4)V`
`"Time"=("longer side (length)")/("velocity")=(8xx10^(-2))/(0.01)`
t=8s.