240Chapt. 31Faraday’s Law of Induction and Inductorswherer0is a fiducial (or reference) radius andt0is a fiducial (or reference) time. Att= 0, theloop has radius zero. Att=t0, the loop has radiusr0.a) What is the magnetic flux Φ due to the applied field linked by the loop in terms of thegiven variablesB,r0,t, andt0?b) What is magnitude of the induced emfEin the loop in terms of the given variablesB,r0,t, andt0? What is theSENSEof the emf (i.e., what is the direction of current flowthat it would cause) when viewing the loop in the direction of the applied B-field?HINT:Remember Lenz’s law. Calculate the time-averaged induced emf first if you need to.c) Given that the loop has constant resistanceR, what is the power dissipated in the loop bythe induced current in in terms of the given variablesB,r0,t,t0, andR?d) What is the total energy dissipatedEdis(i.e., lost to heat by the resistance) in the loop inthe interval fromt= 0 totin terms of the given variablesB,r0,t,t0andR?
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