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CHAPTER 29 ELECTROMAGNETIC INDUCTION BASIC CONCEPTS Faraday’s Law Lenz’s Law Motional emf 1 Chapter 21: We saw: Electric Charge Produces an Electric Field Chapter 27: We saw: Moving Electric Charge Produces a Magnetic Field 2 Now Changing Magnetic Field Produces an εmf a potential difference (voltage) 3 What is changing and causing the emf is the magnetic flux. In Chapter 22 defined Electric Flux Magnetic Flux is similar 4 Flux through an area We will define a vector to represent area. The direction of the vector will be perpendicular to the surface. The length of the vector will be the area of the surface. The vector will be . 5 The flux will be First, flat area perpendicular to 6 For a surface parallel to 7 And for in between If this flux changes an emf will be induced in the area. 8 Consider a copper coil with one loop B A r For N loops 9 N loops B A r 10 FARADAY’S LAW The emf induced in a circuit is directly proportional to the time rate of change of the magnetic flux through the circuit. Or 11 If changes with time an emf, , will be produced. Coil in magnetic field. 12 Flux through coil Flux can change: 1. Magnitude of changes. 2. Area of loop changes. 13 3. The angle changes. 4. Any combination of the three. 14 Example: Consider a coil with 200 turns on a rectangular frame, 20 cm by 30 cm. The resistance of the coil is 2 Ω. 15 If increases uniformly from zero to in 0.8 s what is the current in the coil? At At ଶ ଶ 16 The current will be 17 Lenz’s Law A changing magnetic flux will cause an emf and if the emf is in a conductor there will be a current. What will be the direction of the current? Lenz’s Law will answer that question. 18 The polarity of the induced emf is such that it tends to produce a current that will create a magnetic flux to oppose the change in magnetic flux through the loop. 19 a. Magnet moves toward loop. Magnet field is down and increasing. Induced emf and thus current will be ccw to oppose the increase. 20 b. Magnet moves away from loop. Magnetic field is up and but decreasing. Induced current gives magnetic field to oppose the decrease. 21 Motional emf dx 22 In time dt the rod will move dx. The area covered in dt will be Faraday’s Law 23 A conducting rod moving in a magnetic field will have an emf Induced across it given by this equation. 24 Example: My airplane Luscombe 8E Built 1947 Wingspan 22 feet = 6.7m Speed 100 mph = 44.7 m/s 25 If I am flying it at a point on earth where the vertical magnetic field is what is the voltage drop across the wings? ିହ ିଶ 26 Book example (A more interesting problem): The small segment magnetic field . is moving in the 27 What we have learned So the contribution to the emf for the small segment is Angular velocity and velocity are related by 28 Add them up – integrate: 29 30 Consider a loop around a long solenoid. The current in the solenoid is increasing so the flux through the loop is increasing. 31 An emf is induced in the loop by Faraday’s Law ಳ Also from Chapter 23 we know the potential difference between two points is ್ ೌ 32 If we integrate around the loop from the galvanometer back to the galvanometer in a counter‐clockwise direction we get the emf induced in the loop 33 But also Therefore One of Maxwell’s Equations. 34