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| 184_notes:pc_potential [2018/05/24 14:15] – dmcpadden | 184_notes:pc_potential [2021/01/26 19:17] (current) – [Potential vs Distance Graphs] bartonmo | ||
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| Some of Sections 16.3, 16.5, and 16.7 in Matter and Interactions (4th edition) | Some of Sections 16.3, 16.5, and 16.7 in Matter and Interactions (4th edition) | ||
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| ===== Electric Potential of a Point Charge ===== | ===== Electric Potential of a Point Charge ===== | ||
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| ==== Potential vs Distance Graphs ==== | ==== Potential vs Distance Graphs ==== | ||
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| Because electric potential is a scalar, it is generally easier to graph than electric field is. Typically, we will still specify a path and graph the electric potential along that path because when you have multiple charges, the electric potential does not necessarily take on the same value or change in the same way in all directions. For a single positive point charge, if we pick a path along any direction moving away from the point charge, we will get the potential vs distance graph that is shown to the right. From the $V=\frac{1}{4\pi\epsilon_0}\frac{q}{r}$ equation, we get a graph that looks very similar to a $y=\frac{1}{x}$ graph. This graph tells us that the closer you get to the point charge, the higher the electric potential; whereas, the only time the electric potential is zero is when $r=\infty$. | Because electric potential is a scalar, it is generally easier to graph than electric field is. Typically, we will still specify a path and graph the electric potential along that path because when you have multiple charges, the electric potential does not necessarily take on the same value or change in the same way in all directions. For a single positive point charge, if we pick a path along any direction moving away from the point charge, we will get the potential vs distance graph that is shown to the right. From the $V=\frac{1}{4\pi\epsilon_0}\frac{q}{r}$ equation, we get a graph that looks very similar to a $y=\frac{1}{x}$ graph. This graph tells us that the closer you get to the point charge, the higher the electric potential; whereas, the only time the electric potential is zero is when $r=\infty$. | ||