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whitepapers:sequences:emsequence:start 2019/07/22 11:56 | whitepapers:sequences:emsequence:start 2019/07/22 11:56 current | ||
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A more in-depth discussion of the rationale, student thinking, and the way these activities fit together can be found in a discussion of how these activities break the learning into manageable [[.:pieces]] | A more in-depth discussion of the rationale, student thinking, and the way these activities fit together can be found in a discussion of how these activities break the learning into manageable [[.:pieces]] | ||

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$$\text{Coordinate Dependent:} \qquad V=\frac{1}{4 \pi \epsilon_0} \int\frac{\lambda |ds'\ \hat s + s'\ d\phi'\ \hat \phi + dz'\ \hat z|}{| s'^2 + s^2 +2ss' \cos(\phi-\phi') + z^2|}$$ | $$\text{Coordinate Dependent:} \qquad V=\frac{1}{4 \pi \epsilon_0} \int\frac{\lambda |ds'\ \hat s + s'\ d\phi'\ \hat \phi + dz'\ \hat z|}{| s'^2 + s^2 +2ss' \cos(\phi-\phi') + z^2|}$$ | ||

Using what you one about the geometry of the source, one can simplify the expression. For example, if the source is a ring of charge with radius $R$ and charge $Q$ in the $x$-, $y$-plane the integral becomes: | Using what you one about the geometry of the source, one can simplify the expression. For example, if the source is a ring of charge with radius $R$ and charge $Q$ in the $x$-, $y$-plane the integral becomes: | ||

- | $$\text{Coordinate and Geometry Dependent:} \qquad V=\frac{1}{4 \pi \epsilon_0}\, \frac{Q}{2\pi} \int_0^{2\pi}\frac{R\ d\phi'}{| R^2 + s^2 +2Rs \cos(\phi-\phi') + z^2|}$$ | + | $$\text{Coordinate and Geometry Dependent:} \qquad V=\frac{1}{4 \pi \epsilon_0}\, \frac{Q}{2\pi R} \int_0^{2\pi}\frac{R\ d\phi'}{| R^2 + s^2 +2Rs \cos(\phi-\phi') + z^2|}$$ |

====Lecture: Chop, Calculate, and Add==== | ====Lecture: Chop, Calculate, and Add==== |