Chapter 31237P31.71The magnetic field produced by the current in the straight wire isperpendicular to the plane of the coil at all points within the coil. Themagnitude of the field is BIr=µπ02. Thus, the flux linkage isNNILdrrNILhwhtBhhwΦ==+FHGIKJ++zµπµπωφ0022maxlnsinbg.Finally, the induced emf isFIG. P31.71εµωπωφεπππωφεπφ= −+FHGIKJ+= −×+FHGIKJ+=−+−−0712141010050 00 200200215 0087 1200NILwhtttmaxlncos..ln.cos.cosbgejafafafejbgafbgmscm5.00 cmmVThe term sinωφt+bgin the expression for the current in the straight wire does not changeappreciably when ωtchanges by 0.10 rad or less. Thus, the current does not change appreciablyduring a time interval∆t<=×−−0 102001 61014..πssej.We define a critical length, c t∆ =××=×−3 00101 6104 810844...mssmejejequal to the distance towhich field changes could be propagated during an interval of 1 6104.×−s. This length is so muchlarger than any dimension of the coil or its distance from the wire that, although we consider the
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