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L15 Electromagnetic induction and inductance L15.1 : Electromagnetic induction Faraday’s law: an electric field is induced (or caused) by a change of magnetic flux. Magnetic flux Lecture outline: Faraday’s law. Induced emf. Lenz’s law. Electric generators and motors. Inductance. Solenoids. Transformers. Induced EMF School of Physics- 2004 1 L15.2 : Electromagnetic induction changing flux here 2 L15.3 : Electromagnetic induction An Electromotive Force (EMF) is induced, because of the change of the magnetic flux. There are 4 different ways of changing the magnetic flux: change current here School of Physics- 2004 move the magnet If B is uniform, If there are N loops of wire in a coil: Total EMF is stretch the coil rotate the coil School of Physics- 2004 3 L15.4 : Electromagnetic induction School of Physics- 2004 where B is the flux through one loop. 4 L15.5 : Electromagnetic induction Consider the rotating loop: Note the minus sign in Faraday’s law: this leads to Lenz’s law: “when the EMF is induced, the current produces a magnetic field to oppose the original change in magnetic flux.” Flux is decreasing Example: eddy currents are produced in conductors that result in a reduction of the change of magnetic flux. velocity of wire down Now along the wire. along the wire, and a So the force on the charge is current flows along the wire, which produces a magnetic field B1: This strengthens the original field, so opposes the change: also i x B produces a force on the wire opposing the motion. Lenz’s law is equivalent to a statement of the conservation of energy for induced EMFs: we do work against the force opposing the change of magnetic flux. Otherwise we’d get a perpetual motion machine! School of Physics- 2004 charge q 5 School of Physics- 2004 6 L15.6 : Electromagnetic induction Electric generator, dynamo: School of Physics- 2004 7 School of Physics- 2004 L15.8 : Electromagnetic induction Electric motors: The inverse of generators, current leads to motion. If the torque is constant, why doesn’t the loop get faster and faster? The rotating loop produces an induced EMF which opposes the original current, and the torque is reduced (a back EMF). So we get a balance between work done and energy dissipated in the circuit. Example: R = 100 8 L15.9 : Inductance The magnetic flux B produced by a current coil is usually proportional to the current: where L is the inductance. (number of turns in coil) in coil, source EMF = 100V, back EMF = 80V. Such a coil is called an inductor. The energy in the inductor is At first, the coil has no rotation, so no change of flux, and no back EMF. Maximum current, i = 100/100 = 1A. Finally, coil has steady rotation, back EMF = 80V, total EMF = 100-80 = 20V. Final current = 20/100 = 0.2A. School of Physics- 2004 9 School of Physics- 2004 L15.10 : Inductance Example: a long solenoid The magnetic field is 10 L15.11 : Inductance Transformers A Consider 2 wires wrapped around an iron core. l and the magnetic flux is Therefore Each wire changes contact with each slip ring half way through each cycle ("commutator") DC generator (car dynamo) Each wire in contact with one slip ring. AC generator (car alternator) L15.7 : Electromagnetic induction AC current (ip) in primary winding gives alternating magnetic flux in core, which gives an induced EMF: & where In the secondary winding there is the same flux, so The energy in the solenoid is therefore so the energy per unit volume is This energy can be regarded as residing in the magnetic field produced by the coil. School of Physics- 2004 Therefore 11 School of Physics- 2004 so we can boost up the voltage by changing the number of turns. 12 L15.12 : Inductance L15.13 : Inductance With a load, there is an AC current (is) in the secondary winding. The power in each winding is , so If R is the resistance in the secondary, So Contact breaker closed, current in primary magnetizes core. Contact breaker open, collapse of B gives high induced voltage in secondary. which is the effective load seen in the primary winding. School of Physics- 2004 13 School of Physics- 2004 14