184_notes:comp_super

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184_notes:comp_super [2017/08/31 14:55] – dmcpadden184_notes:comp_super [2018/01/18 22:18] – dmcpadden
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 +Section 15.9 in Matter and Interactions (4th edition)
 +
 ===== Superposition and the Computer ===== ===== Superposition and the Computer =====
  
-The principle of superposition is an overarching and powerful tool in much of physics. It is useful well beyond the electric field as you will see with the magnetic field (and as you might see in future physics courses in quantum mechanics). The fact that the electric field obeys the principle of superposition defines a powerful algorithm for computing the electric field at any given location from any distribution of charge. In these notes, you will read about how that algorithm works.+The principle of superposition is an overarching and powerful tool in much of physics. It is useful well beyond the electric field as you will see with the magnetic field (and as you might see in future physics courses in quantum mechanics). The fact that the electric field obeys the principle of superposition means we can define a powerful algorithm for computing the electric field at any given location from any distribution of charge. In these notes, you will read about how you can structure code to calculate the electric field from many sources charge (though you could apply this procedure to electric potential as well).
  
 ==== The Superposition Principle ==== ==== The Superposition Principle ====
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 $$\vec{E}_{net} = \sum \vec{E}_i = \vec{E}_1 + \vec{E}_2 + \vec{E}_3 + \dots$$ $$\vec{E}_{net} = \sum \vec{E}_i = \vec{E}_1 + \vec{E}_2 + \vec{E}_3 + \dots$$
 +
 +where $\vec{E}_1$ would be the electric field from one point charge, $\vec{E}_2$ would be the electric field from a second point charge, and so on. For this week, we will focus on superposition of point charges, but 
  
 You have seen how this principle can be used to find the electric field due to point charges and how it has been used for "continuous charge distributions" like the line charge example. In the line charge example, you sliced up the line into little bits, which each contributed a small amount of electric field $d\vec{E}$ at a given location. The total electric field at that same given location was the integral (continuous sum) of the contributions, You have seen how this principle can be used to find the electric field due to point charges and how it has been used for "continuous charge distributions" like the line charge example. In the line charge example, you sliced up the line into little bits, which each contributed a small amount of electric field $d\vec{E}$ at a given location. The total electric field at that same given location was the integral (continuous sum) of the contributions,
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 These somewhat monotonous steps will give us an approximate value for the electric field at the point of interest. The smaller the chunks, the better the approximation. You can probably see why setting up a computer to do this makes a lot of sense. Computers are really good at doing the same calculation over and over again! These somewhat monotonous steps will give us an approximate value for the electric field at the point of interest. The smaller the chunks, the better the approximation. You can probably see why setting up a computer to do this makes a lot of sense. Computers are really good at doing the same calculation over and over again!
  
-So if we want to compute the electric field at a given location due to a distribution of charges, the algorithm is just cutting the distribution into chunks, computing the electric field of each chunk as a point charge, and adding all the contributions together. This is a form of [[https://en.wikipedia.org/wiki/Numerical_integration|numerical integration]], which is a powerful technique in computational science. The pseudocode for this algorithm is the following:+So if we want to compute the electric field at a given location due to a distribution of charges, the algorithm is just cutting the distribution into chunks, computing the electric field of each chunk as a point charge, and adding all the contributions together. This is a form of [[https://en.wikipedia.org/wiki/Numerical_integration|numerical integration]], which is a powerful technique in computational science. As a tool for thinking through these computational algorithms, we will sometimes write out the steps we want the computer to take in plain words rather than code - this is called **pseudocode**. The pseudocode for the electric field algorithm above is the following:
  
 <code> <code>
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 </code> </code>
  
 +You can also use pseudocode (and may have already) to help you plan and understand the code you are writing.
  • 184_notes/comp_super.txt
  • Last modified: 2021/02/09 19:08
  • by bartonmo