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Ch0219

# Ch0219 - Chapter 19 Induction Transformers and Generators...

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Chapter 19 Induction, Transformers, and Generators 157 19 Induction, Transformers, and Generators In this chapter we provide examples chosen to further familiarize you with Faraday’s Law of Induction and Lenz’s Law. The last example is the generator, the device used in the world’s power plants to convert mechanical energy into electrical energy. Example 19-1 A straight wire carries a current due northward. Due east of the straight wire, at the same elevation as the straight wire, is a horizontal loop of wire. The current in the straight wire is increasing. Which way is the current, induced in the loop by the changing magnetic field of the straight wire, directed around the loop? Solution I’m going to draw the given situation from a few different viewpoints, just to help you get used to visualizing this kind of situation. As viewed from above-and-to-the-southeast, the configuration (aside from the fact that magnetic field lines are invisible) appears as: where I included a sheet of paper in the diagram to help you visualize things. East North Up I increasing B increasing

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Chapter 19 Induction, Transformers, and Generators 158 Here’s a view of the same configuration from the south, looking due north: Both diagrams make it clear that we have an increasing number of downward-directed magnetic field lines through the loop. It is important to keep in mind that a field diagram is a diagrammatic manner of conveying information about an infinite set of vectors. There is no such thing as a curved vector. A vector is always directed along a straight line. The magnetic field vector is tangent to the magnetic field lines characterizing that vector. At the location of the loop, every magnetic field vector depicted in the diagram above is straight downward. While it is okay to say that we have an increasing number of magnetic field lines directed downward through the loop, please keep in mind that the field lines characterize vectors . In presenting my solution to the example question, “What is the direction of the current induced in a horizontal loop that is due east of a straight wire carrying an increasing current due north?” I wouldn’t draw either one of the diagrams above. The first one takes too long to draw and there is no good way to show the direction of the current in the loop in the second one. The view from above is the most convenient one: I increasing B increasing Loop Viewed Edge-on Up Down East West B increasing I increasing NORTH SOUTH EAST WEST
Chapter 19 Induction, Transformers, and Generators 159 In this view (in which the downward direction is into the page) it is easy to see that what we have is an increasing number of downward-directed magnetic field lines through the loop (more specifically, through the region enclosed by the loop). In its futile attempt to keep the number of magnetic field lines directed downward through the loop the same as what it was, PIN B harpoonrightnosp must be directed upward in order to cancel out the newly-appearing downward-directed magnetic field lines.

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