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Question

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 s1 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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Solution

Length of the rectangular wire, l=8cm=0.08m

Width of the rectangular wire, b=2cm=0.02m

Hence, area of the rectangular loop,

A=lb

=0.08×0.02

=16×104m2

Magnetic field strength, B=0.3T

Velocity of the loop, v=1cm/s=0.01m/s


(a)

Emf developed in the loop is given as:

e=Blv

=0.3×0.08×0.01=2.4×104V

Time taken to travel along the width, t=DistancetravelledVelocity=bv

=0.020.01=2s

Hence, the induced voltage is 2.4×104V which lasts for 2 s.


(b)

Emf developed, e=Bbv

=0.3×0.02×0.01=0.6×104V

Time taken to travel along the length, t=DistancetraveledVelocity=lv

=0.080.01=8s

Hence, the induced voltage is 0.6×104V which lasts for 8 s.


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