EDUC 215 Chapter 9, Fall 2009

Chapter 22 Electromagnetic Induction Outline 1. Induced Emf and Induced Current 2. Motional Emf 3. Magnetic Flux 4. Faraday’s Law of Electromagnetic Induction 5. Lenz’s Law 6. Application of Electromagnetic Induction to the Reproduction of Sound 7. The Electric Generator 8. Mutual Inductance and Self- Inductance 9. Transformers 1- Induced Emf and Induced Current There are a number of ways a magnetic field can be used to generate an electric current. It is the changing field that produces the current. The current in the coil is called the induced current because it is brought about by a changing magnetic field. Since a source emf is always needed to produce a current, the coil behaves as if it were a source of emf. This emf is known as the induced emf. An emf can be induced by changing the area of a coil in a constant magnetic field In each example, both an emf and a current are induced because the coil is part of a complete circuit. If the circuit were open, there would be no induced current, but there would be an induced emf. The phenomena of producing an induced emf with the aid of a magnetic field is called electromagnetic induction. Each charge within the conductor is moving and experiences a magnetic force qvB F  The separated charges on the ends of the conductor give rise to an induced emf, called a motional emf. 2 - Motional emf vBL E Motional emf when v, B, and L are mutually perpendicular Example 1 Operating a Light Bulb with Motional Emf Suppose the rod is moving with a speed of 5.0m/s perpendicular to a 0.80-T magnetic field. The rod has a length of 1.6 m and a negligible electrical resistance. The rails also have a negligible electrical resistance. The light bulb has a resistance of 96 ohms. Find (a) the emf produced by the rod and (b) the current induced in the circuit. (a)     V 4.6 m 6.1 .0 80 T m s 0.5  vBL  E .0 067 A 96 V 4.6   I R  E (b) Motional emf and Electrical Energy In order to keep the rod moving at constant velocity, the force the hand exerts on the rod must balance the magnetic force on the current: ILB F F  hand  Conceptual Example 3 Conservation of Energy A conducting rod is free to slide down between two vertical copper tracks. There is no kinetic friction between the rod and the tracks. Because the only force on the rod is its weight, it falls with an acceleration equal to the acceleration of gravity. Suppose that a resistance connected between the tops of the tracks. (a) Does the rod now fall with the acceleration of gravity? (b) How does the principle of conservation of energy apply? 3- Magnetic Flux The Magnetic flux is defined as: cos B B A B A      is the angle between B and the normal to the plane. A is the area of the loop. B is the magnetic force. • When the field is perpendicular to the plane of the loop, as in a, θ = 0 and ΦB = ΦB, max = BA • When the field is parallel to the plane of the loop, as in b, θ = 90° and ΦB = 0 • The flux can be negative, for example if θ = 180° • SI units of flux are T m² = Wb (Weber) 4- Faraday’s law of electromagnetic induction If a circuit contains N tightly wound loops and the flux changes by during a time interval t, the average emf induced is given by Faraday’s Law: B N t     Example 5 The Emf Induced by a Changing Magnetic Field A coil of wire consists of 20 turns each of which has an area of 0.0015 m2. A magnetic field is perpendicular to the surface. Initially, the magnitude of the magnetic field is 0.050 T and 0.10s later, it has increased to 0.060 T. Find the average emf induced in the coil during this time.      10 V 0.3 s 0.10 .0 050 T .0 060 T cos 0 .0 0015 m 20 cos cos cos 3 2                        t B B NA t B A N BA t N o o    E 5 - Lenz’ Law Currents are produced in the loop to counteract changes in flux. Conceptual Example 9 The Emf Produced by a Moving Copper Ring. There is a constant magnetic field directed into the page in the shaded region. The field is zero outside the shaded region. A copper ring slides through the region. For each of the five positions, determine whether an induced current exists and, if so, find its direction. 6 – Applications of Electromagnetic Induction to the Reproduction of Sound 7- The Electric Generator BLvsin v BL    E   2 W r v   Emf induced in a rotational planar coil t t NAB o    sin sin E E    f  2 t o E E sin The Electrical energy delivered and the countertorque When the generator is delivering current, there is a magnetic force acting on the coils. The magnetic force gives rise to a countertorque that opposes the rotational motion. The back emf generated by an electric motor When a motor is operating, two sources of emf are present: (1) the applied emf V that provides current to drive the motor, and (2) the emf induced by the generator-like action of the rotating coil. R V I  E  Consistent with Lenz’s law, the induced emf acts to oppose the applied emf and is called back emf. Example 12 Operating a Motor The coil of an ac motor has a resistance of 4.1 ohms. The motor is plugged into an outlet where the voltage is 120.0 volts (rms), and the coil develops a back emf of 118.0 volts (rms) when rotating at normal speed. The motor is turning a wheel. Find (a) the current when the motor first starts up and (b) the current when the motor is operating at normal speed. 29 A 4.1 0 V 120 V       R V I E (a) .0 49 A 4.1 120 V 118 0. V       R V I E (b) 8- Mutual Inductance and Self- inductance The changing current in the primary coil creates a changing magnetic flux through the secondary coil, which leads to an induced emf in the secondary coil. The effect in called mutual induction. t N   E  Emf due to mutual induction t I M     p sE mutual inductance SI Unit of mutual inductance: 1H (Henry) 1V s A   The effect in which a changing current in a circuit induces and emf in the same circuit is referred to as self induction. Self-Inductance SI Unit of self inductance: 1H (Henry) 1V s A   t I L    E self inductance The energy stored in an inductor Energy stored in an inductor Energy density 2 2 1 Energy LI  2 2 1 Energy density B  o 9- Transformers A transformer is a device for increasing or decreasing an ac voltage. t N    s sE t N    p pE p s p s N E  N E p s p s N N V V  Transformer equation s p s p p s N N V V I I   A transformer that steps up the voltage simultaneously steps down the current, and a transformer that steps down the voltage steps up the current.