10-0 10 1010-1 Chapter 10 Faraday’s Law of Induction !10.1! Faraday’s Law of Induction ............................................................................. 10-3!10.1.1! Magnetic Flux ........................................................................................... 10-5!10.2! Motional EMF .................................................................................................. 10-5!10.3! Faraday’s Law (see also Faraday’s Law Simulation in Section 10.13) ........... 10-8!10.3.1! Example Induced Electric Field ................................................................ 10-9!10.4! Lenz’s Law ..................................................................................................... 10-12!10.4.1! Magnets and Conducting Loop Movies .................................................. 10-15!10.4.2! Example Bar Moving Along Rails in a Constant Magnetic Field .......... 10-16!10.5! Generators ...................................................................................................... 10-17!10.6! Eddy Currents ................................................................................................. 10-19!10.7! Summary ........................................................................................................ 10-20!10.8! Appendix: Induced Emf and Reference Frames ............................................. 10-20!10.9! Problem-Solving Tips: Faraday’s Law and Lenz’s Law ................................ 10-22!10.10!Solved Problems ............................................................................................. 10-22!10.10.1!Rectangular Loop Near a Wire ............................................................... 10-22!10.10.2!Loop Changing Area ............................................................................... 10-24!10.10.3!Sliding Rod ............................................................................................. 10-25!10.10.4!Moving Bar ............................................................................................. 10-26!10.10.5!Time-Varying Magnetic Field ................................................................ 10-27!10.10.6!Moving Loop .......................................................................................... 10-28!10.11!Conceptual Questions ..................................................................................... 10-30!10.12!Additional Problems ....................................................................................... 10-31!10.12.1!Sliding Bar .............................................................................................. 10-31!10.12.2!Sliding Bar on Wedges ........................................................................... 10-31!10.12.3!RC Circuit in a Magnetic Field ............................................................... 10-32!10.12.4!Sliding Bar .............................................................................................. 10-33!10.12.5!Rotating Bar ............................................................................................ 10-33!10-2 10.12.6!Rectangular Loop Moving Through Magnetic Field .............................. 10-34!10.12.7!Magnet Moving Through a Coil of Wire ................................................ 10-34!10.12.8!Alternating-Current Generator ................................................................ 10-35!10.12.9!EMF Due to a Time-Varying Magnetic Field ......................................... 10-36!10.12.10! Falling Loop ..................................................................................... 10-37!10.13!Faraday’s Law Simulation .............................................................................. 10-38!10-3 Faraday’s Law of Induction 10.1 Faraday’s Law of Induction The electric fields and magnetic fields considered up to now have been produced by stationary charges and moving charges (currents), respectively. Imposing an electric field on a conductor gives rise to a current that in turn generates a magnetic field. One could then inquire whether or not an electric field could be produced by a magnetic field. In 1831, Michael Faraday discovered that, by varying a magnetic field with time, an electric field could be generated. The phenomenon is known as electromagnetic induction. Figure 10.1.1 illustrates one of Faraday’s experiments, and Figure 10.1.1 shows one frame from a movie of the actual experiment. Figure 10.1.1 Electromagnetic induction Faraday showed that no current is registered in the galvanometer when bar magnet is stationary with respect to the loop. However, a current is induced in the loop when a relative motion exists between the bar magnet and the loop. In particular, the galvanometer deflects in one direction as the magnet approaches the loop, and the opposite direction as it moves away. There is an interactive simulation of this aspect of Faraday’s Law in Section 10.13 below.10-4 Faraday’s experiment demonstrates that an electric current is induced in the loop by changing the magnetic field. The coil behaves as if it were connected to an emf source. Experimentally it is found that the induced emf depends on the rate of change of magnetic flux through the coil. http://youtu.be/tb6LywqnhBI Figure 10.1.2 Electromagnetic induction experiment (a) http://youtu.be/vcG2wv6IZ8k (b) http://youtu.be/NWE9SCRgBv0 Figure 10.1.3 Visualizations of the total magnetic field when (a) the magnet is moving toward the coil and (b) when the magnet is moving away from the coil. Figure 10.1.3 shows a visualization of the total magnetic field in this experiment, that is the field due the magnet itself and to the magnetic field generated by the induced currents in the coil. Whether we are moving the magnet into the coil or out of the coil, we see that the total magnetic field is such that the magnetic field lines tend to get “hung up” momentarily in trying to move through the coil. This is an example of Lenz’s Law, as discussed in Section 10.4 below. We now explore how we can quantitatively describe this phenomena in mathematical terms. To do this we must introduce the concept of magnetic flux.10-5 10.1.1 Magnetic Flux Consider a uniform magnetic field passing
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