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www.GOALias.blogspot.comPhysicsThe two effects add up since both cause a decrease in flux alongthe positive z-direction. Therefore, induced emf = 12.96 × 10 –5 V;induced current = 2.88 × 10 –2 A. The direction of induced currentis such as to increase the flux through the loop along positivez-direction. If for the observer the loop moves to the right, thecurrent will be seen to be anti-clockwise. A proper proof of theprocedure above is as follows:aΦ () t = aB( x,)dt x0adΦ d Bxt ( , )= a dxdtdtusing,dB ∂ B ∂B dx= +dt ∂t ∂x dt∂= B ∂+ vB∂t∂ xwe get,0ad Φ Bxt ( , ) Bxt ( , )= a dx ∂ + v∂dt ∂t ∂ x0where A = a 2∂B∂ B= A + v∂t∂ xThe last step follows because∂ B∂t,∂ B∂xand v are given to beconstants in the problem. Even if you do not understand this formalproof (which requires good familiarity with calculus), you will stillappreciate that flux change can occur both due to the motion of theloop as well as time variations in the magnetic field.6.13 Q = Idtt fti= 1R=−tftiNRε dtΦfΦidΦ300= N(i f)R Φ −Φfor N = 25, R = 0.50 Ω, Q = 7.5 × 10 –3 CΦ f= 0, A = 2.0 × 10 –4 m 2 , Φ i= 1.5 × 10 –4 WbB = Φ i/A = 0.75 T