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A wire of length is charged to a uniform linear charge density . Let r be the distance from the wire of a point located on the perpendicular bisector of the wire. (a) Assuming , compute the electric field as a function of r. (b) Compare your answer to the exact expression for the electric field. What should the ratio be so that the error you make is less than 1%? (c) Using Gauss’s law, compute the electric field of the wire for . (d) Compare your result to the exact expression for the electric field. What should the ratio be so that the error you make is less than 1%?
There is an interesting optical effect you have likely noticed while driving along a flat stretch of road on a sunny day. A small, distant dip in the road appears to be filled with water. You may even see the reflection of an oncoming car. But, as you get closer, you find no puddle of water after all; the shimmering surface vanishes, and you see nothing bu empty road. It was only a mirage, the name for this phenomenon. The mirage is due to the different index of refraction of hot and cool air. The actual bending of the light rays that produces the mirage is subtle, but we can make a simple model as follows. When air is heated, its density decreases and so its index of refraction. Consequently, a pocket of hot air in a dip in a road has a lower index of refraction than the cooler air above it. Incident light rays with large angles of incidence experience total internal reflection. The mirage that you see is due to this reflection. As you get nearer, the angle goes below the critical angle and there is no more total internal reflection; the "water" disappears! Which of these changes would allow you to get closer to the mirage before it vanishes? A. Making the pocket of hot air nearer in temperature to the air above it. B. Looking for the mirage on a windy day, which mixes the air layers C. Increasing the difference in temperature between the pocket of hot air and the air above it. D. Looking at it from a greater height above the ground.