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Question: worksheet computing the y component of the electric field generated...

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Worksheet Computing the y component of the Electric Field generated from a continuous charge distribution. Christos Velissaris, January 10, 2017 Name(s): Problem: A rod of length L carries total charge a that is uniformly charge distributed over the length of the rod. Therefore the charge distribution at the rod A (charge per unit length) is given by the formula da We consider a point P located at distance Lfrom the center of the rod (see figure below). We are being asked to calculate the ycomponent of the produced by this uniform charge distribution at Electric Field point P. Critical Thinking and Solution Methodology: Although we have a formula giving us the direction and the magnitude of the Electric Field produced by a point like charge at distancerfrom we do not know of any specific formula capable to give us the magnitude and the direction (x and y components) of the Electric Field produced by a continuous charge distribution. Therefore we have to devise one from what we already know. We will attempt to find an approximate solution by making the assumption that the uniformly distributed charge along the rod, behaves like a point-like charge Q concentrated at the center of the rod. (Intuitively we fell that this is a reasonable assumption is the point-like charge q is far away from the rod compared to the rod length). Perfectionists and mathematically inclined students might protest that the method very method. We and the obtained result is very incorrect. That is why will little more sophisticated a point- will keep splitting the into smaller and smaller pieces replacing each piece of the rod with rod like charge at the center of the piece. we will then calculate the net y component of the Electric Field produced at point P. we feel that every time we increase the number of bar pieces and every Intuitively time the bar pieces become smaller and smaller the more accurate results we get. You have to show all your work and attach to this worksheet any scrap paper y used with your computations. After you finish with your calculations fill the blank at the answer line (the s indicates the number of segments you have split the r to obtain your approximate answer). More specifically in this worksheet do the following:
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