The horizontal axis is the ratio of the distance to the rod divided by the length of the rod. Number of pieces (for the numerical calculation) = 100.I want to plot the magnitude of the electric field as a distance from the rod for all three methods (the two equations and the numerical method). The second formula is an approximation if the length of the rod is long compared to the distance from the rod. Lets first combine F qE and Coulombs Law. Skipping the derivation, I have two expressions for the magnitude of the electric field along an axis perpendicular to the center of the rod. The net charge represented by the entire length of the rod could then be expressed as Q lamda L. This is a region that I can also calculate the electric field using calculus such that I can see how well the two methods agree. In order to determine the accuracy of this numerical model, I need to calculate the electric field along an axis perpendicular to the rod and in the center of the rod. In this paper, we present an electric field analysis for the optimal structural design of lightning rods for high performance with a charge transfer system. That looks very pretty, but it's not that useful. However, I will show you what it looks like. There are probably many introductory physics classes that use this problem as part of a homework assignment or something. I know, that sort of stinks - but that's the way things are going to be. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. Use the information below to generate a citation. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the For any cross sectional area if a normal is drawn on it. E E A cos - (i) Electric field intensity. Greater the electric field lines passing greater is electric flux and is represented by E and is given by relation. Our first step is to define a charge density for a charge distribution along a line, across a surface, or within a volume, as shown in Figure 5.22. Number of electric lines of forces passing through a certain area is called electric flux. This is exactly the kind of approximation we make when we deal with a bucket of water as a continuous fluid, rather than a collection of H 2 O H 2 O molecules. However, in most practical cases, the total charge creating the field involves such a huge number of discrete charges that we can safely ignore the discrete nature of the charge and consider it to be continuous. Note that because charge is quantized, there is no such thing as a “truly” continuous charge distribution. Faraday’s Law of Induction and Lenz’ Law. We simply divide the charge into infinitesimal pieces and treat each piece as a point charge. If a charge distribution is continuous rather than discrete, we can generalize the definition of the electric field. This is in contrast with a continuous charge distribution, which has at least one nonzero dimension. The charge distributions we have seen so far have been discrete: made up of individual point particles.
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