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 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 =16×10−4m2 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=2.4×10−4V Time taken to travel along the width, t=VelocityDistancetravelled=vb =0.010.02=2s Hence, the induced voltage is 2.4×10−4V which lasts for 2 s. (b) Emf developed, e=Bbv =0.3×0.02×0.01=0.6×10−4V Time taken to travel along the length, t=VelocityDistancetraveled=vl =0.010.08=8s Hence, the induced voltage is 0.6×10−4V which lasts for 8 s.
