Class 12 Physics
CBSE and UP Board
Electromagnetic Induction
Chapter-6 Exercise 6.4
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?
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Length of the rectangular wire, 1 = 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 x 0.02 = 16 x 10⁻4 m2
Magnetic field strength, B = 0.3 T
Velocity of the loop, v = 1 cm/s = 0.01 m/s
Ans (a).
Emf developed in the loop is given as :
e =Blv = 0.3 x 0.08 x 0.01
= 2.4 x 10⁻⁴ V
Time taken to travel along the width ,
l = Distance travelled /(Velocity) = b/v= 0.02 /0.01 = 2 s
Hence, the induced voltage is 2.4 x 10-4 V which lasts for 2 s.
Ans (b).
Emf developed, e = Bbv = 0.3 x 0.02 x 0.01 = 0.6 x 10⁻4 V
Time taken to travel along the length, t =Distance traveled /Velocity =l/v
=0.08/0.01 = 8 s
Hence, the induced voltage is 0.6 x 10-4 V which lasts for 8 s.
(a] Emf developed in the loop is given as:
e=Blv = 0.3×0.08×0.01
= 2.4 x 10-4 V