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184_notes:comp_super [2017/08/31 15:04] – dmcpadden | 184_notes:comp_super [2018/05/29 14:58] – [Superposition and the Computer] curdemma | ||
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Section 15.9 in Matter and Interactions (4th edition) | Section 15.9 in Matter and Interactions (4th edition) | ||
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+ | [[184_notes: | ||
===== 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 | + | 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 |
==== 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. |
$$\vec{E}_{net} = \sum \vec{E}_i = \vec{E}_1 + \vec{E}_2 + \vec{E}_3 + \dots$$ | $$\vec{E}_{net} = \sum \vec{E}_i = \vec{E}_1 + \vec{E}_2 + \vec{E}_3 + \dots$$ | ||
- | 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 " | + | 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 |
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- | $$\vec{E}_{net} = \int d\vec{E}$$ | + | |
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- | [[184_notes: | + | |
==== 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 |
- | - 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 |