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Ch0218

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Chapter 18 Faraday's Law, Lenz's Law 145 18 Faraday's Law, Lenz's Law Do you remember Archimedes’s Principle? We were able to say something simple, specific, and useful about a complicated phenomenon. The gross idea was that a submerged object being pressed upon on every surface element in contact with fluid, by the fluid, experiences a net upward force because the pressure in a fluid is greater at greater depth. The infinite sum, over all the surface area elements of the object in contact with the fluid, of the force of magnitude pressure-times-the-area, and direction normal to and into the area element, resulted in an upward force that we called the buoyant force. The thing is, we were able to prove that the buoyant force is equal in magnitude to the weight of that amount of fluid that would be where the object is if the object wasn’t there. Thus we can arrive at a value for the buoyant force without having to even think about the vector integration of pressure-related force that causes it. We are about to encounter another complicated phenomenon which can be characterized in a fruitful fashion by a relatively simple rule. I’m going to convey the idea to you by means of a few specific processes, and then sum it up by stating the simple rule. Consider a gold 1 ring and a bar magnet in the hands of a person. The person is holding the ring so that it encircles the bar magnet. She is holding the magnet, north end up. There is a magnetic field, due to the bar magnet, within the bar magnet, and in the region of space around it. 1 Any conductive material will do here. I chose gold arbitrarily. N S N S

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Chapter 18 Faraday's Law, Lenz's Law 146 It is important to note that the magnetic field lines are most densely packed inside the bar magnet. Now suppose that the person, holding the magnet at rest in one hand, moves the loop upward. I want to focus on what is going on while she is moving it upward. As she moves the loop upward, she is moving it roughly along the direction of the magnetic file lines, but, and this is actually the important part, that loop will also be “cutting through” some magnetic field lines. Consider an instant in time when the loop is above the magnet, and moving upward: From above, the scene looks like: where it is important to realize that none of those magnetic field lines begin on the magnet or end at the tip of the arrow depicted, rather, they extend out of the magnet toward us, flower out and over, back down away from us, and then they loop around to enter the south pole of the magnet from which they extend back up through the magnet toward us. In fact, no magnetic field line ever begins or ends anywhere. They all form closed loops. This is a manifestation of the fact that there is no such thing as magnetic charge. (There are no magnetic monopoles.) N S v v B
Chapter 18 Faraday's Law, Lenz's Law 147 Here’s where we’re going with this: The motion of the ring relative to the magnet is going to cause a current in the ring. Here’s how:

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