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Lecture 10-1 Motional EMF Most of the worlds electric energy is produced by electric generators, not by batteries. Motional emf is the principle behind the electric generator. Motional emf occurs whenever a conductor moves, cutting through magnetic fields. Assume that a conducting rod of length L moves with velocity v in magnetic field B . This creates a force on the conduction electrons in the rod. L v F B av qv B per electron on average FB accumulates conduction electrons near bottom. In response E develops, opposing the accumulation. Equilibrium is reached when F E qE F B E v B Potential difference between the ends of rod induced emf More generally, V EL vBL V EL v B L Lecture 10-2 Motional EMF of Sliding Conductor Induced EMF + v FM vBL L Direction of current is as if the induced emf were due to a battery. counter-clockwise here (later: Lenz’s Law) Rod slides as before, but there is a complete circuit instead of a rod. • Induced emf moves electrons (current flows). • emf (and current) is maintained as long as the rod is sliding with v. Magnitude of induced current I vBL I R R Magnetic force FM acts on this I vB 2 L2 FM I LB R FM decelerates the bar Lecture 10-3 Faraday’s Law (See Giambattista V.2 Ch.20, p726-744) Hans C. Oersted discovered that electric current produces a magnetic field. Michel Faraday showed the reverse: Magnetic field produces an electric current. Induced emf of ε=vBL turns out to be just an example of a more general result: Faraday’s Law of Induction: The magnitude of the induced emf in conducting loop is equal to the rate at which the magnetic flux through the surface spanned by the loop changes with time. B t Magnetic flux B BdA S B cos dA S 1 Wb = 1 T m2 • First decide on which way the loop is to be taken Fixes sign of B by RHR • The positive direction for emf is relative to the chosen loop direction Lecture 10-4 Kinds of Ways to Change Magnetic Flux? B BA cos • Changing the magnitude of the field within a conducting loop (or coil). • Changing the area of the loop (or coil) that lies within the magnetic field. • Changing the relative orientation of the field and the loop. motor generator Lecture 10-5 Conducting Loop in a Changing Magnetic Field Induced EMF has a direction such that it opposes the change in magnetic flux that produced it. approaching Magnetic moment created by induced currrent I repels the bar magnet. Force on ring is repulsive. moving away Magnetic moment created by induced currrent I attracts the bar magnet. Force on ring is attractive. Lecture 10-6 Faraday’s and Lenz’s Laws Faraday’s Law of Induction: The magnitude of the induced emf in conducting loop is equal to the rate at which the magnetic flux through the surface spanned by the loop changes with time. B t Lenz’s Law: The direction of induced emf and current opposes the change that produced them. At 1, 3, and 5, B is not changing. So there is no induced emf. At 2, B is increasing into page. So emf is induced to produce a counterclockwise current. At 4, B in decreasing into page. So current is clockwise. Lecture 10-7 Applications Ground fault interupter Audio tape playback head Moving coil microphone Lecture 10-8 Examples of Induction + - Switch has been open for some time: Switch is just closed: Nothing happening EMF induced in Coil 2 + - Switch is just opened: EMF is induced again Switch is just closed: EMF is induced in coil - + Back emf (counter emf) Lecture 10-9 Physics 219 – Question 1 – Sept. 26. 2016. There are two circular loop wires with z-axis going through their centers perpendicularly as shown. A current I1 flows in the top loop, clockwise as viewed from +z direction and its magnitude is increasing. Which statement is true about I2, the induced current in the bottom loop? z a) Clockwise b) Counter-clockwise c) I2 is zero. I1 y x I2 Lecture 10-10 Transformer • AC voltage can be stepped up or down by using a transformer. •AC current in the primary coil creates a time-varying magnetic flux through the secondary coil via the iron core. This induces emf in the secondary circuit. 2 1 N1 N2 ideal transformer (no losses and magnetic flux per turn is the same on primary and secondary). (With no load) B 2 N2 t B 1 N1 t 2 N2 1 N1 N1 N 2 V1 V2 turns ratio N1 N 2 V1 V2 step-up step-down Lecture 10-11 Energy Transfer in a Transformer With switch S closed: conservation of energy proportional to average power I1 I1V1 I 2 V2 N1 V1 N 2 V2 I2 N1 I 2 N 2 I1 Lecture 10-12 Eddy Current A current induced in a solid conducting object, due to motion of the object in an external magnetic field. The pattern of eddy currents is usually complicated, but Lenz’s Law implies that the resultant force opposes the motion which caused it. • The presence of eddy current in the object results in dissipation of electric energy that is derived from mechanical motion of the object. • The dissipation of electric energy in turn causes the loss of mechanical energy of the object, i.e., the presence of the field damps motion of the object.