188CHAPTER 20 20.33(a) When a coil having Nturns and enclosing area Arotates at angular frequency ωin a constant magnetic field, the emf induced in the coil is maxmaxsinwhere tNBA⊥==EEE55.0 TBHere, is the magnitude of the magnetic field perpendicular to the rotation axis of the coil. In the given case, B⊥µ⊥=; Aabπ=where ( )10.0 cm2a=and ( )4.b=00 cm2; and rev1 m100 1min60.0()in0.5s=2ωπ2rad sfThus, 610.055.010T0.040 0 m10.5 rad s4−=×maxE0.100 mor 51.8110V18.1 Vmax−=E(b) When the rotation axis is parallel to the field, then 0B⊥=giving max0=EIt is easily understood that the induced emf is always zero in this case if you recognize that the magnetic field lines are always parallel to the plane of the coil, and the flux through the coil has a constant value of zero.
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