184_notes:comp_super

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184_notes:comp_super [2017/08/31 15:04] – dmcpadden184_notes:comp_super [2018/01/18 22:18] – dmcpadden
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 ===== 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,
  • 184_notes/comp_super.txt
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