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Unformatted text preview: Physics 4B Lecture Notes 31-1 Chapter 31 - Induction and Inductance Problem Set #10 - due: Ch 31 - 1, 5, 11, 28, 35, 43, 51, 59, 70, 74, 83, 100 Lecture Outline 1. Faraday's Law of Induction 2. Motors and Generators 3. The Meissner Effect and Superconductivity 4. The Definition of Mutual Inductance 5. The Definition of Self Inductance 6. The LR Circuit 7. Energy Storage in Inductors and B-fields Magnet, wire, coil, & galvanometer (moving the coil vs. moving the magnet - it can't matter!) 1. Faraday's Law of Induction Moving a wire through the field causes the charges within the wire to feel an upward magnetic force, r F = q r r B F = q B. Positive charges accumulate at the top of the wire and negative charges at the bottom. This creates a downward electric field in the wire. The net force on the charges is given by the Second Law, F = ma q B- qE = ma. Charges move upward until a=0. The electric field is then, E = B. If the wire was rolling along some rails connected to a voltmeter, the meter would give a reading due to the electric field in the wire. This voltage can be found from the E-field, V = - r E d r s V = E l V = B l . Moving through a magnetic field creates a potential difference just like a battery would. Example 1: Estimate the induced voltage across the 40.0m wingspread of an airplane traveling 800km/h (222m/s) perpendicular to the earths magnetic field of 50.0T. Using the Second Law when the charges in the wing have reached equilibrium, F = ma q B- qE = E = B . The induced voltage can be found from the E-field, V = - r E d r s V = E l V = B l . V = B l (50.0 T)(40.0m)(222m/s) 0.444V F e + F m ++- - V l F F e + F m ++- - Physics 4B Lecture Notes 31-2 The other way to look at this is to think about it in terms of the changing magnetic flux in the loop. The potential difference between the ends is, V = B l . Using the definition of velocity, V = B l dx dt = B d dt l x ( 29 = B dA dt = d dt BA ( 29 = d B dt . This explains why moving the magnet creates a voltage just like moving the wire does. If the wire has N turns then the voltage is N times bigger. Notice that the current flows in a direction such as to fight the change in the field. This is called "Lenz's Rule." Putting all this together gives Faraday's Law, = - N d B dt Faraday's Law where we have defined the magnetic flux as, B r B d r A The Definition of Magnetic Flux Beyond the Mechanical Universe (vol. 37 Ch 11,12,15,18,21,28) Example 2: A small loop of N turns and area A is in the same plane as a long straight wire carrying a current i = i o sin t . Find the induced voltage in the loop as a function of time and show that the peak-to-peak voltage is proportional to the peak magnetic field....
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