Q 4. A rectangular wire loop of sides 8 cm and 2 cm with a small cut is moving out of a region of the 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?
Length of the wired loop, l = 8 cm = 0.08 m
Width of the wired loop, b = 2 cm = 0.02 m
Hence, the area of the röctangular loop, A=lb=0.08×0.02=16×10−4m2
Strength of magnetic field, B = 0.2 T
Velocity of the loop, v = 1 cm / s = 0.01 m / s
(a)Emf developed in the loop is given as:
e=Blv=0.3×0.08×0.01 =2.4×10−4V
Time taken to travel along the width, t= Distance travelled Velocity =bv =0.020.01=2s
Hence, the induced voltage is 2.4 x 10-4 V which lasts for 2 s.
(b) Emf developed,
e=Bbv=0.3×0.02×0.01=0.6×10−4VHence, the induced voltage is 0.6×10−4 V0.6×10-4 V">0.6×10−4V which lasts for 8 s.
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