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www.GOALias.blogspot.comElectromagneticInductionor current in a loop is through a change in theloop’s orientation or a change in its effective area.As the coil rotates in a magnetic field B, theeffective area of the loop (the face perpendicularto the field) is A cos θ, where θ is the anglebetween A and B. This method of producing aflux change is the principle of operation of asimple ac generator. An ac generator convertsmechanical energy into electrical energy.The basic elements of an ac generator areshown in Fig. 6.16. It consists of a coil mountedon a rotor shaft. The axis of rotation of the coilis perpendicular to the direction of the magneticfield. The coil (called armature) is mechanicallyrotated in the uniform magnetic field by someexternal means. The rotation of the coil causesthe magnetic flux through it to change, so anemf is induced in the coil. The ends of the coilare connected to an external circuit by meansFIGURE 6.16 AC Generatorof slip rings and brushes.When the coil is rotated with a constantangular speed ω, the angle θ between the magnetic field vector B and thearea vector A of the coil at any instant t is θ = ωt (assuming θ = 0º at t = 0).As a result, the effective area of the coil exposed to the magnetic field lineschanges with time, and from Eq. (6.1), the flux at any time t isΦ B= BA cos θ = BA cos ωtFrom Faraday’s law, the induced emf for the rotating coil of N turns isthen,dΦBdε = – N = – NBA (cos ω t )dt dtThus, the instantaneous value of the emf isε = NBA ωsin ωt (6.21)where NBAω is the maximum value of the emf, which occurs whensin ωt = ±1. If we denote NBAω as ε 0, thenε = ε 0sin ωt (6.22)Since the value of the sine fuction varies between +1 and –1, the sign, orpolarity of the emf changes with time. Note from Fig. 6.17 that the emfhas its extremum value when θ = 90º or θ = 270º, as the change of flux isgreatest at these points.The direction of the current changes periodically and therefore the currentis called alternating current (ac). Since ω = 2πν, Eq (6.22) can be written asε = ε 0sin 2π ν t (6.23)where ν is the frequency of revolution of the generator’s coil.Note that Eq. (6.22) and (6.23) give the instantaneous value of the emfand ε varies between +ε 0and –ε 0periodically. We shall learn how todetermine the time-averaged value for the alternating voltage and currentin the next chapter.225