Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
10/23/2011 Chapter 23 Magnetic Flux and Faraday’s Law of Induction Units of Chapter 23 • Induced Electromotive Force • Magnetic Flux • Faraday’s Law of Induction • Lenz’s Law • Mechanical Work and Electrical Energy • Generators and Motors • Inductance and RL Circuits • Energy Stored in a Magnetic Field • Transformers Copyright © 2010 Pearson Education, Inc. 23-1 Induced Electromotive Force Faraday’s experiment: closing the switch in the primary circuit induces a current in the secondary circuit, but only while the current in the primary circuit is changing. Copyright © 2010 Pearson Education, Inc. 23-1 Induced Electromotive Force • The current in the secondary circuit is zero as long as the current in the primary circuit, and therefore the magnetic field in the iron bar, is not changing. • Current flows in the secondary circuit while the current in the primary is changing. It flows in opposite directions depending on whether the magnetic field is increasing or decreasing. • The magnitude of the induced current is proportional to the rate at which the magnetic field is changing. Copyright © 2010 Pearson Education, Inc. Copyright © 2010 Pearson Education, Inc. 23-1 Induced Electromotive Force 23-2 Magnetic Flux Note the motion of the magnet in each image: Magnetic flux is used in the calculation of the induced emf. B=0.035 T. Find the magnetic flux through this loop. Copyright © 2010 Pearson Education, Inc. Copyright © 2010 Pearson Education, Inc. 1 10/23/2011 23-3 Faraday’s Law of Induction Faraday’s law: An emf is induced only when the magnetic flux through a loop changes with time. 23-3 Faraday’s Law of Induction There are many devices that operate on the basis of Faraday’s law. Electric generator What is the induced emf in at t=0.05s, 0.15s, and 0.50s? Tape reader Copyright © 2010 Pearson Education, Inc. Copyright © 2010 Pearson Education, Inc. 23-4 Lenz’s Law 23-4 Lenz’s Law Lenz’s Law An induced current always flows in a direction that opposes the change that caused it. Therefore, if the magnetic field is increasing, the magnetic field created by the induced current will be in the opposite direction; if decreasing, it will be in the same direction. This conducting rod completes the circuit. As it falls, the magnetic flux decreases, and a current is induced. The force due to the induced current is upward, slowing the fall. Copyright © 2010 Pearson Education, Inc. Copyright © 2010 Pearson Education, Inc. 23-4 Lenz’s Law 23-5 Mechanical Work and Electrical energy Motional emf Currents can also flow in bulk conductors. These induced currents, called eddy currents, can be powerful brakes. Change in flux: Induced emf: Copyright © 2010 Pearson Education, Inc. Copyright © 2010 Pearson Education, Inc. 2 10/23/2011 23-5 Mechanical Work and Electrical Energy If the rod is to move at a constant speed, an external force must be exerted on it. This force should have equal magnitude and opposite direction to the magnetic force: 23-5 Mechanical Work and Electrical Energy The mechanical power delivered by the external force is: Compare this to the electrical power in the light bulb: Therefore, mechanical power has been converted directly into electrical power. Copyright © 2010 Pearson Education, Inc. 23-6 Generators and Motors An electric generator converts mechanical energy into electric energy: Copyright © 2010 Pearson Education, Inc. 23-6 Generators and Motors The induced emf in a rotating coil varies sinusoidally: An outside source of energy is used to turn the coil, thereby generating electricity. Copyright © 2010 Pearson Education, Inc. Copyright © 2010 Pearson Education, Inc. 23-6 Generators and Motors An electric motor is exactly the opposite of a generator – it uses the torque on a current loop to create mechanical energy. Copyright © 2010 Pearson Education, Inc. 23-7 Inductance When the switch is closed in this circuit, a current is established that increases with time. Copyright © 2010 Pearson Education, Inc. 3 10/23/2011 23-7 Inductance Inductance is the proportionality constant that tells us how much emf will be induced for a given rate of change in current: 23-7 Inductance Given the definition of inductance, the inductance of a solenoid can be calculated: When used in a circuit, such a solenoid (or other coil) is called an inductor. Solving for L, Copyright © 2010 Pearson Education, Inc. Copyright © 2010 Pearson Education, Inc. 23-8 RL Circuits 23-8 RL Circuits This shows the current in an RL circuit as a function of time: ε I = (1 − e −t / τ ) R The time constant is: When the switch is closed, the current immediately starts to increase. The back emf in the inductor is large, as the current is changing rapidly. As time goes on, the current increases more slowly, and the potential difference across the inductor decreases. Copyright © 2010 Pearson Education, Inc. Copyright © 2010 Pearson Education, Inc. 23-9 Energy Stored in a Magnetic Field It takes energy to establish a current in an inductor; this energy is stored in the inductor’s magnetic field. Considering the emf needed to establish a particular current, and the power involved, we find: Copyright © 2010 Pearson Education, Inc. Example Consider the circuit shown in the figure below. Take ε = 6.00 V, L = 8.00 mH, and R = 4.00 Ω. (a) What is the inductive time constant of the circuit? (b) Calculate the current in the circuit 250 μs after the switch is closed. (c) What is the value of the final steady-state current? (d) How long does it take the current to reach 80.0% of its maximum value? Copyright © 2010 Pearson Education, Inc. 4 10/23/2011 23-10 Transformers A transformer is used to change voltage in an alternating current from one value to another. By applying Faraday’s law of induction to both coils, we find: Copyright © 2010 Pearson Education, Inc. 23-10 Transformers The power in both circuits must be the same; therefore, if the voltage is lower, the current must be higher. When transmitting electric power over long distances, it is most economical to use high voltage and low current, because this minimizes I2R power losses. Copyright © 2010 Pearson Education, Inc. Summary of Chapter 23 • A changing magnetic field can induce a current in a circuit. The magnitude of the induced current depends on the rate of change of the magnetic field. • Magnetic flux: • Faraday’s law gives the induced emf: Summary of Chapter 23 • Lenz’s law: an induced current flows in the direction that opposes the change that created the current. • Motional emf: • emf produced by a generator: • An electric motor is basically a generator operated in reverse. • Inductance occurs when a coil with a changing current induces an emf in itself. Copyright © 2010 Pearson Education, Inc. Copyright © 2010 Pearson Education, Inc. Summary of Chapter 23 • Definition of inductance: Summary of Chapter 23 • Current in an RL circuit after closing the switch: • Inductance of a solenoid: • An RL circuit has a characteristic time constant: Copyright © 2010 Pearson Education, Inc. • Transformer equation: Copyright © 2010 Pearson Education, Inc. 5