Review Faraday s Law of Induction in words is The magnitude of the Vemf induced in a conducting loop is equal to the time rate of change of the magnetic flux from the loop This induced emf tends to oppose the flux change Physics for Scientists Engineers 2 Faraday s Law of Induction in equation form is Vemf Spring Semester 2005 d B dt Vemf is the induced voltage Lecture 26 d B dt is time rate change of the magnetic flux The negative sign means that the induced voltage opposes the change in flux March 1 2005 Physics for Scientists Engineers 2 1 March 1 2005 Review 2 The third special case of our simple induction processes is the technologically by far the most interesting It is the variation of the angle between the loop and the magnetic field with time while keeping the area of the loop as well as the magnetic field strength constant in time We leave the area of the loop and its orientation relative to the magnetic field constant but vary the magnetic field in time dB dt We leave the magnetic field as well as the orientation of the loop relative to the magnetic field constant but change the area of the loop that is exposed to the magnetic field B constant Vemf B cos In this way Faraday s Law of Induction can be applied to the generation and use of electric current A device that produces electric current from mechanical motion is called a generator dA dt We leave the magnetic field constant and keep the area of the loop fixed as well but allow the angle between the two to change as a function of time A device that produces mechanical motion from electric current is called a motor A B constant Vemf ABsin March 1 2005 Physics for Scientists Engineers 2 2 Generators and Motors If we have a flat loop we can keep two of the three variables A B constant and vary the third then we can have the following three special cases A constant Vemf A cos Physics for Scientists Engineers 2 3 March 1 2005 Physics for Scientists Engineers 2 4 Generators and Motors 2 Generators and Motors 3 A simple generator consists of a loop forced to rotate in a fixed magnetic field In a direct current generator the rotating coil is connected to an external circuit using a split commutator ring The driving force that causes the loop to rotate can be supplied by hot steam running over a turbine As the coil turns the connection is reversed such that the induced voltage always has the same sign Or the loop can be made to rotate by water or wind in a completely pollution free way of generating electrical power In alternating current generator each end of the loop is connected to the external circuit through a slip ring Thus this generator produces an induced voltage that varies from positive to negative and back and is called an alternator Direct current generator split ring commutator March 1 2005 The voltages and currents produced by these generators are illustrated to the right Alternating current generator slip ring commutator Physics for Scientists Engineers 2 5 March 1 2005 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 a voltage opposing the voltage that is being supplied to create current in the motor You might have noticed that when a large electric motor such as an air conditioner compressor starts up the lights dim because the 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 large amounts of current that could produce enough heat to damage the motor Physics for Scientists Engineers 2 Alternating voltage current Physics for Scientists Engineers 2 6 Lenz s Law Another fact of life concerning electric motors is back emf March 1 2005 Direct voltage current Lenz s Law defines a rule for determining the direction of an induced current in a loop An induced current will have a direction such that the magnetic field due to the induced current opposes the change in the magnetic flux that induces the current The direction of the induced current corresponds to the direction of the induced emf We can apply Lenz s Law to the situations described in yesterday s lecture 7 March 1 2005 Physics for Scientists Engineers 2 8 Lenz s Law 2 Lenz s Law Four Cases The physical situation shown here involves moving a magnet toward a loop with the north pole pointed toward the loop The magnetic field lines point toward the north pole of the magnet a An increasing magnetic field pointing to the left induces a current that creates a magnetic field to the right As the magnet moves toward the loop the magnitude of the field increases in the direction pointing toward the north pole b An increasing magnetic field pointing to the right induces a current that creates a magnetic field to the left Lenz s law states that a current is induced in the loop that tends to oppose the change in magnetic flux c A decreasing magnetic field pointing to the left induces a current that creates a magnetic field to the left This induced magnetic field then points in the opposite direction as the field from the magnet d A decreasing magnetic field pointing to the right induces a current that creates a magnetic field to the right March 1 2005 Physics for Scientists Engineers 2 9 March 1 2005 Eddy Currents Physics for Scientists Engineers 2 10 Eddy Currents 2 We observe that the pendulum with the solid metal sheet stops in the gap of the magnet while the grooved sheet passes through the magnetic field only slowing slightly Let s consider two pendulums each with a non magnetic conducting metal plate at the end that is designed to pass through the gap of a strong permanent magnet This demonstration illustrates the very important concept of induced eddy currents One metal plate is solid and the other has slots cut in it As the pendulum with the solid plate enters the magnetic field Lenz s law tells us that the changing magnetic flux will induce currents that tend to oppose the change in flux These currents interact with the magnetic field to stop the pendulum For the slotted plate the induced eddy currents are blocked and the slotted plate passes through the magnetic field only slowing We pull back both pendulums and release them March 1 2005 Physics for Scientists Engineers 2 11 March 1 2005 Physics for Scientists Engineers 2 12 Eddy Currents 3 Induced Electric Fields Eddy currents are not like the current
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