A rectangular loop of sides 8 cm and 2 cm with a small cut is moving out of a region of uniform megnetic field of magnitude 0.3 tesla directed normal to the loop. What is the voltage developed acorss the cut if velocity of the loop is `1 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?

Explanation

Length of the rectangular wire, l = 8 cm = 0.08 m
Width of the rectangular wire, b = 2 cm = 0.02 m
Hence, area of the rectangular loop,
A = lb
= `0.08 xx 0.02`
`= 16 × 10^(−4) m^(2)`
Magnetic field strength, B = 0.3 T
Velocity of the loop, v = 1 cm/s = 0.01 m/s
(a) Emf developed in the loop is given as:
e = Blv
`= 0.3xx0.08xx0.01 = 2.4xx10^(−4) V`
Time taken to travel along the width,t=`("Distance travelled")/("Velocity")=b/v`
`=0.02/0.01=2 s`
Hence, the induced voltage is `2.4xx10^(−4)` V which lasts for 2 s.
(b) Emf developed, e = Bbv
`= 0.3 xx 0.02 xx 0.01 = 0.6 xx 10^(−4)` V
Time taken to trvel along the length,l=`("Distance traveled")/("Velocity")=l/v`
=`0.08/0.01= 8 s`
Hence, the induced voltage is 0.6 × 10−4 V which lasts for 8 s.