March 1, 2005 Physics for Scientists&Engineers 2 1Physics for Scientists &Physics for Scientists &EngineersEngineers 22Spring Semester 2005Lecture 26March 1, 2005 Physics for Scientists&Engineers 2 2ReviewReview! Faraday’s Law of Induction in words is•The magnitude of the Vemf induced in a conducting loop is equal tothe time rate of change of the magnetic flux from the loop. Thisinduced emf tends to oppose the flux change.! Faraday’s Law of Induction in equation form is•Vemf is the induced voltage•d!B/dt is time rate change of the magnetic flux• The negative sign means that the induced voltage opposes thechange in fluxVemf= !d"BdtMarch 1, 2005 Physics for Scientists&Engineers 2 3Review (2)Review (2)! If we have a flat loop, we can keep two of the threevariables (A,B,") constant, and vary the third, then we canhave the following three special cases• We leave the area of the loop and its orientation relative to themagnetic field constant, but vary the magnetic field in time• We leave the magnetic field as well as the orientation of the looprelative to the magnetic field constant, but change the area of theloop that is exposed to the magnetic field• We leave the magnetic field constant and keep the area of the loopfixed as well, but allow the angle between the two to change as afunction of timeA,! constant: Vemf= " A cos!dBdtB,! constant: Vemf= " B cos!dAdtA, B constant: Vemf=!ABsin"March 1, 2005 Physics for Scientists&Engineers 2 4Generators and MotorsGenerators and Motors! The third special case of our simple induction processes isthe technologically by far the most interesting! It is the variation of the angle between the loop and themagnetic field with time, while keeping the area of the loopas well as the magnetic field strength constant in time! In this way, Faraday’s Law of Induction can be applied tothe generation and use of electric current! A device that produces electric current from mechanicalmotion is called a generator! A device that produces mechanical motion from electriccurrent is called a motorMarch 1, 2005 Physics for Scientists&Engineers 2 5Generators and Motors (2)Generators and Motors (2)! A simple generator consists of a loop forced to rotate in a fixedmagnetic field! The driving force that causes the loop to rotate can be supplied by hotsteam running over a turbine! Or the loop can be made to rotate by water or wind in a completelypollution-free way of generating electrical powerDirect current generatorsplit ring commutatorAlternating current generatorslip ring commutatorMarch 1, 2005 Physics for Scientists&Engineers 2 6Generators and Motors (3)Generators and Motors (3)! In a direct current generator the rotating coil is connectedto an external circuit using a split commutator ring! As the coil turns, the connection is reversed such that theinduced voltage always has the same sign! In alternating current generator, each end of the loop isconnected to the external circuit through a slip ring• Thus this generator produces an induced voltage that varies frompositive to negative and back, and is called an alternator! The voltages and currentsproduced by thesegenerators areillustrated to the rightDirect voltage/currentAlternating voltage/currentMarch 1, 2005 Physics for Scientists&Engineers 2 7Back EMFBack EMF! Another fact-of-life concerning electric motors is back emf! An electric motor is essentially the same as an electric generator! Thus as the motor runs faster and faster, it begins to generate avoltage opposing the voltage that is being supplied to createcurrent in the motor! You might have noticed that when a large electric motor such asan air conditioner compressor starts up, the lights dim, becausethe motor is drawing a large amount of current! As the motor speeds up, the dimming effect disappears! When the motor is running at normal speed, it draws less current! If an electric motor is overloaded and stops, it will draw largeamounts of current that could produce enough heat to damagethe motorMarch 1, 2005 Physics for Scientists&Engineers 2 8LenzLenz’’s Laws Law! Lenz’s Law defines a rule for determining thedirection of an induced current in a loop! An induced current will have a direction such thatthe magnetic field due to the induced currentopposes the change in the magnetic flux thatinduces the current! The direction of the induced current correspondsto the direction of the induced emf! We can apply Lenz’s Law to the situationsdescribed in yesterday’s lectureMarch 1, 2005 Physics for Scientists&Engineers 2 9LenzLenz’’s Law (2)s Law (2)! The physical situation shown hereinvolves moving a magnet toward aloop with the north pole pointedtoward the loop! The magnetic field lines pointtoward the north pole of the magnet! As the magnet moves toward theloop, the magnitude of the field increases in the directionpointing toward the north pole! Lenz’s law states that a current is induced in the loop thattends to oppose the change in magnetic flux! This induced magnetic field then points in the oppositedirection as the field from the magnetMarch 1, 2005 Physics for Scientists&Engineers 2 10LenzLenz’’s Law - Four Casess Law - Four Cases!a) An increasing magnetic field pointing to the left inducesa current that creates a magnetic field to the right!b) An increasing magnetic field pointing to the rightinduces a current that creates a magnetic field to the left!c) A decreasing magnetic field pointing to the left inducesa current that creates a magnetic field to the left!d) A decreasing magnetic field pointing to the right inducesa current that creates a magnetic field to the rightMarch 1, 2005 Physics for Scientists&Engineers 2 11Eddy CurrentsEddy Currents! Let’s consider two pendulums, each with a non-magneticconducting metal plate at the end that is designed to passthrough the gap of a strong permanent magnet! One metal plate is solid and the other has slots cut in it! We pull back both pendulums and release themMarch 1, 2005 Physics for Scientists&Engineers 2 12Eddy Currents (2)Eddy Currents (2)! We observe that the pendulum with the solid metal sheetstops in the gap of the magnet while the grooved sheetpasses through the magnetic field, only slowing slightly! This demonstration illustrates the very important conceptof induced eddy currents! As the pendulum with the solid plate enters the magneticfield, Lenz’s law tells us that the changing magnetic fluxwill induce currents that tend to oppose the change in
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