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 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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Solution

## Length of the rectangular wire, l=8cm=0.08mWidth of the rectangular wire, b=2cm=0.02mHence, area of the rectangular loop,A=lb=0.08×0.02=16×10−4m2Magnetic field strength, B=0.3TVelocity 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=2.4×10−4VTime taken to travel along the width, t=DistancetravelledVelocity=bv =0.020.01=2sHence, the induced voltage is 2.4×10−4V which lasts for 2 s.(b)Emf developed, e=Bbv=0.3×0.02×0.01=0.6×10−4VTime taken to travel along the length, t=DistancetraveledVelocity=lv =0.080.01=8sHence, the induced voltage is 0.6×10−4V which lasts for 8 s.

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