Lightning ReviewNext week: Prof. Claude Pruneau20.5 GeneratorsAC GeneratorsAC generatorAC generator (cont)DC generatorMotorsMotors and Back emfExample: coil in magnetic field20.6 Eddy currents (application)20.7 Self-inductanceExample: solenoid20.9 Energy stored in a magnetic fieldExample: stored energy1110/14/200310/14/2003General Physics (PHY 2140)Lecture 18Lecture 18¾ Electricity and Magnetism9Induced voltages and induction9Generators and motors9Self-inductionChapter 20http://www.physics.wayne.edu/~apetrov/PHY2140/2210/14/200310/14/2003Lightning ReviewLightning Review02IBrµπ=Last lecture:1.1.Induced voltages and inductionInduced voltages and induction99Induced EMFInduced EMF99Faraday’s lawFaraday’s law99Motional EMFcosBAθΦ=Nt∆Φ=−∆EMotional EMFBlv=EReview Problem: Two very long, fixed wires cross each other perpendicularly. They do not touch but are close to each other, as shown. Equal currents flow in the wires, in the directions shown. Indicate the locus of points where the net magnetic field is zero.3310/14/200310/14/2003Next week: Prof. Claude Next week: Prof. Claude PruneauPruneauLectures on Monday and WednesdayExam on Friday4410/14/200310/14/200320.5 Generators20.5 GeneratorsGenerators and motors are two of the most important Generators and motors are two of the most important applications of induced applications of induced emfemf(magnetic inductance). (magnetic inductance). A generator is something that converts mechanical A generator is something that converts mechanical energy to electrical energy. energy to electrical energy. Alternating Current (AC) generatorAlternating Current (AC) generatorDirect Current (DC) generatorDirect Current (DC) generatorA motor does the opposite, it converts electrical energy A motor does the opposite, it converts electrical energy to mechanical energy. to mechanical energy.5510/14/200310/14/2003AC GeneratorsAC GeneratorsBasic operation of the generatorBasic operation of the generatorAs the As the loop rotatesloop rotates, the , the magnetic magnetic flux through it changesflux through it changeswith timewith timeThis This induces an emfinduces an emfand a and a current in the external circuitcurrent in the external circuitThe ends of the loop are The ends of the loop are connected to slip rings that rotate connected to slip rings that rotate with the loopwith the loopConnections to the external Connections to the external circuit are made by stationary circuit are made by stationary brushed in contact with the slip brushed in contact with the slip ringsrings6610/14/200310/14/2003AC generatorAC generatorCompute EMFCompute EMFIt is only generated in BC It is only generated in BC and DA wiresand DA wiresEMF generated in BC and EMF generated in BC and DA would beDA would beThus, total EMF isThus, total EMF isIf the loop is rotating with If the loop is rotating with ωABCDωvv sin θBlv⊥==BC DAEEB22sinBlv Blvθ⊥==EA2sin 2 sin2aBlv t Bl tωωω==Eas v=rω=aω/27710/14/200310/14/2003AC generator (cont)AC generator (cont)Generalize the result to N loopsGeneralize the result to N loopswhere we also noticed that where we also noticed that A=laA=laNote: Note: is is reached when reached when ωωt=90t=90˚˚or 270or 270˚˚(loop (loop parallel to the magnetic field)parallel to the magnetic field)sinNBA tωω=ENBAω=maxEEMF generated by the AC generator8810/14/200310/14/2003DC generatorDC generatorBy a clever change to the rings and brushes By a clever change to the rings and brushes of the ac generator, we can create a dc of the ac generator, we can create a dc generator, that is, a generator where the generator, that is, a generator where the polarity of the polarity of the emfemfis always positive. is always positive. The basic idea is to use The basic idea is to use a single split ring a single split ring instead of two complete ringsinstead of two complete rings. The split ring . The split ring is arranged so that, just as the is arranged so that, just as the emfemfis about is about to change sign from positive to negative, the to change sign from positive to negative, the brushes cross the gap, and the polarity of brushes cross the gap, and the polarity of the contacts is switched. the contacts is switched. The polarity of the contacts changes in The polarity of the contacts changes in phase with the polarity of the phase with the polarity of the emfemf----the two the two changes essentially cancel each other out, changes essentially cancel each other out, and the and the emfemfremains always positive. remains always positive. The The emfemfstill varies still varies sinusoidallysinusoidallyduring each during each half cycle, but every half cycle is a positive half cycle, but every half cycle is a positive emfemf. .9910/14/200310/14/2003MotorsMotorsA motor is basically a generator running in reverse. A A motor is basically a generator running in reverse. A current is passed through the coil, producing a torque current is passed through the coil, producing a torque and causing the coil to rotate in the magnetic field. Once and causing the coil to rotate in the magnetic field. Once turning, the coil of the motor generates a turning, the coil of the motor generates a back back emfemf, just , just as does the coil of a generator. The back as does the coil of a generator. The back emfemfcancels cancels some of the applied some of the applied emfemf, and limits the current through , and limits the current through the coil. the coil.101010/14/200310/14/2003Motors and Back emfMotors and Back emfThe phrase The phrase back emfback emfis used is used for an emf that tends to reduce for an emf that tends to reduce the applied currentthe applied currentWhen a motor is turned on, When a motor is turned on, there is no back emf initiallythere is no back emf initiallyThe current is very large The current is very large because it is limited only by because it is limited only by the resistance of the coilthe resistance of the coil111110/14/200310/14/2003Example: coil in magnetic fieldExample: coil in magnetic fieldA coil of area 0.10 m² is rotating at 60 rev/s with its axis of A coil of area 0.10 m² is rotating at 60 rev/s with its axis of rotation rotation perpendicular to a 0.20T magnetic field. (a) If there are 1000 tperpendicular to a 0.20T magnetic field. (a) If there are 1000 turns on urns on the coil, what is the maximum voltage induced in the coil? (b) Wthe coil, what