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 isNNILdrrNILhwhtBhΦ==+FHGIKJ++zωφ0022maxlnsinbg.Finally, the induced emf isFIG. P31.71εµωππεπφ=−+FHGIKJ+×+FHGIKJ++−−07121410100 50 0 0 2002002150087 1200NILwhtttmaxlncos..ln.cos.cosejafafafafm scm5.00 cmmVThe term sint+in 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<=×−−01020016 1014..ss.We define a critical length, ct∆=××=×−3001016104810844.mssmejequal to the distance towhich field changes could be propagated during an interval of 16 104.×−s . This length is so muchlarger than any dimension of the coil or its distance from the wire that, although we consider thestraight wire to be infinitely long, we can also safely ignore the field propagation effects in the
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This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .