Transcript Lecture_10
Chapter 29 Electromagnetic Induction and Faraday’s Law Copyright © 2009 Pearson Education, Inc. Faraday’s Law dB d d A B A B cos dt dt dt IR BUT is NOT a conservative potential Copyright © 2009 Pearson Education, Inc. 29-3 EMF Induced in a Moving Conductor This image shows another way the magnetic flux can change: R Copyright © 2009 Pearson Education, Inc. 29-3 EMF Induced in a Moving Conductor B t x t B; A outward dB Bv I R dt Bv I R I 2 FI I B I B B v R Copyright © 2009 Pearson Education, Inc. ConcepTest 29.9 Motional EMF A conducting rod slides on a conducting track in a constant 1) clockwise B field directed into the page. 2) counterclockwise What is the direction of the 3) no induced current induced current? x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x v ConcepTest 29.9 Motional EMF A conducting rod slides on a conducting track in a constant 1) clockwise B field directed into the page. 2) counterclockwise What is the direction of the 3) no induced current induced current? The B field points into the page. The flux is increasing since the area is increasing. The induced B field opposes this change and therefore points out of the page. Thus, the induced current runs counterclockwise, according to the right-hand rule. x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x v x x x x x x x x x x x Follow-up: What direction is the magnetic force on the rod as it moves? 29-3 EMF Induced in a Moving Conductor The induced emf has magnitude This equation is valid as long as B, l, and v are mutually perpendicular (if not, it is true for their perpendicular components). Copyright © 2009 Pearson Education, Inc. 29-3 EMF Induced in a Moving Conductor The induced current is in a direction that tends to slow the moving bar Conductor _ w _ Copyright © 2009 Pearson Education, Inc. 29-3 EMF Induced in a Moving Conductor Fe e v B e v B e Ee v B w Copyright © 2009 Pearson Education, Inc. w 29-3 EMF Induced in a Moving Conductor Example 29-6: Does a moving airplane develop a large emf? An airplane travels 1000 km/h in a region where the Earth’s magnetic field is about 5 x 10-5 T and is nearly vertical. What is the potential difference induced between the wing tips that are 70 m apart? Copyright © 2009 Pearson Education, Inc. 29-4 Electric Generators A generator is the opposite of a motor – it transforms mechanical energy into electrical energy. This is an ac generator: The axle is rotated by an external force such as falling water or steam. The brushes are in constant electrical contact with the slip rings. Copyright © 2009 Pearson Education, Inc. 29-4 Electric Generators If the loop is rotating with constant angular velocity ω, the induced emf is sinusoidal: For a coil of N loops, Copyright © 2009 Pearson Education, Inc. 29-4 Electric Generators Example 29-9: An ac generator. The armature of a 60-Hz ac generator rotates in a 0.15-T magnetic field. If the area of the coil is 2.0 x 10-2 m2, how many loops must the coil contain if the peak output is to be V0 = 170 V? Copyright © 2009 Pearson Education, Inc. 29-4 Electric Generators A dc generator is similar, except that it has a split-ring commutator instead of slip rings. Copyright © 2009 Pearson Education, Inc. ConcepTest 29.10 Generators A generator has a coil of wire rotating in a magnetic field. If the rotation rate increases, 1) increases 2) decreases how is the maximum output 3) stays the same voltage of the generator 4) varies sinusoidally affected? ConcepTest 29.10 Generators A generator has a coil of wire rotating in a magnetic field. If the rotation rate increases, 1) increases 2) decreases how is the maximum output 3) stays the same voltage of the generator 4) varies sinusoidally affected? The maximum voltage is the leading term that multiplies sin wt and is given by e0 = NBAw. Therefore, if w increases, then e0 must increase as well. e NBA w sin( wt ) 29-5 Back EMF and Counter Torque; Eddy Currents An electric motor turns because there is a torque on it due to the current. We would expect the motor to accelerate unless there is some sort of drag torque. That drag torque exists, and is due to the induced emf, called a back emf. Copyright © 2009 Pearson Education, Inc. 29-5 Back EMF and Counter Torque; Eddy Currents Example 29-10: Back emf in a motor. The armature windings of a dc motor have a resistance of 5.0 Ω. The motor is connected to a 120-V line, and when the motor reaches full speed against its normal load, the back emf is 108 V. Calculate (a) the current into the motor when it is just starting up, and (b) the current when the motor reaches full speed. Copyright © 2009 Pearson Education, Inc. 29-5 Back EMF and Counter Torque; Eddy Currents Conceptual Example 29-11: Motor overload. When using an appliance such as a blender, electric drill, or sewing machine, if the appliance is overloaded or jammed so that the motor slows appreciably or stops while the power is still connected, the device can burn out and be ruined. Explain why this happens. Copyright © 2009 Pearson Education, Inc. 29-5 Back EMF and Counter Torque; Eddy Currents A similar effect occurs in a generator – if it is connected to a circuit, current will flow in it, and will produce a counter torque. This means the external applied torque must increase to keep the generator turning. Copyright © 2009 Pearson Education, Inc. 29-5 Back EMF and Counter Torque; Eddy Currents Induced currents can flow in bulk material as well as through wires. These are called eddy currents, and can dramatically slow a conductor moving into or out of a magnetic field. Copyright © 2009 Pearson Education, Inc. 29-6 Transformers and Transmission of Power A transformer consists of two coils, either interwoven or linked by an iron core. A changing emf in one induces an emf in the other. The ratio of the emfs is equal to the ratio of the number of turns in each coil: Copyright © 2009 Pearson Education, Inc. 29-6 Transformers and Transmission of Power This is a step-up transformer – the emf in the secondary coil is larger than the emf in the primary: Copyright © 2009 Pearson Education, Inc. 29-6 Transformers and Transmission of Power Energy must be conserved; therefore, in the absence of losses, the ratio of the currents must be the inverse of the ratio of turns: Copyright © 2009 Pearson Education, Inc. 29-7 A Changing Magnetic Flux Produces an Electric Field A changing magnetic flux induces an electric field; this is a generalization of Faraday’s law. The electric field will exist regardless of whether there are any conductors around: . Copyright © 2009 Pearson Education, Inc. 29-7 A Changing Magnetic Flux Produces an Electric Field Example 29-14: E produced by changing B B. A magnetic field B between the pole faces of an electromagnet is nearly uniform at any instant over a circular area of radius r0. The current in the windings of the electromagnet is increasing in time so that B changes in time at a constant rate dB/dt B at each point. Beyond the circular region (r > r0), we assume B B = 0 at all times. Determine the electric field E at any point P a distance r from the center of the circular area due to the changing B B. Copyright © 2009 Pearson Education, Inc. HW # 10 Chapter 29 – 32, 38, 50, 70 Copyright © 2009 Pearson Education, Inc.