184_notes:comp_super

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184_notes:comp_super [2018/01/18 22:18] – dmcpadden184_notes:comp_super [2018/05/15 14:50] – curdemma
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 Section 15.9 in Matter and Interactions (4th edition) Section 15.9 in Matter and Interactions (4th edition)
 +
 +[[184_notes:dipole_sup|Previous Page: Dipole Superposition Example]]
  
 ===== Superposition and the Computer ===== ===== Superposition and the Computer =====
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 ==== The Superposition Principle ==== ==== The Superposition Principle ====
  
-As a reminder, the principle of superposition states that the electric field at any given location in space is determined by vector sum of the electric field due to each charge that contributes.+The principle of superposition states that the electric field at any given location in space is determined by vector sum of the electric field due to each charge that contributes.
  
 $$\vec{E}_{net} = \sum \vec{E}_i = \vec{E}_1 + \vec{E}_2 + \vec{E}_3 + \dots$$ $$\vec{E}_{net} = \sum \vec{E}_i = \vec{E}_1 + \vec{E}_2 + \vec{E}_3 + \dots$$
  
-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  +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 and how we can model a line of charge using points. (Next week we will use the idea of superposition to model a continuous line of charge and other distribution of charges.)
- +
-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, +
- +
-$$\vec{E}_{net} = \int d\vec{E}$$ +
- +
-[[184_notes:linecharge|There are more details to this calculation in the notes]] on computing field due to a line charge.+
  
 ==== How can we use a computer for this? ==== ==== How can we use a computer for this? ====
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 Let's think through the process for computing the electric field due to a distribution of charges: Let's think through the process for computing the electric field due to a distribution of charges:
  
-  - Cut the distribution up into small chunks +  - Identify the "chunks" of charge that you will treat as point charges
-  - Pick a chunk to treat as a point charge+
   - Compute the electric field due to that chunk at the specified location   - Compute the electric field due to that chunk at the specified location
   - Write down or otherwise keep track of that value   - Write down or otherwise keep track of that value
  • 184_notes/comp_super.txt
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