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| 184_notes:pc_force [2021/01/26 21:28] – [General Relationship] bartonmo | 184_notes:pc_force [2021/01/27 15:57] (current) – [Two Point Charges] bartonmo |
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| $$\vec{F}_{1 \rightarrow 2}=\frac{1}{4\pi\epsilon_0}\frac{q_{1}q_{2}}{(r_{1 \rightarrow 2})^3}\vec{r}_{1 \rightarrow 2}=\frac{1}{4\pi\epsilon_0}\frac{q_{1}q_{2}}{(r_{1 \rightarrow 2})^2}\hat{r}_{1 \rightarrow 2}$$ | $$\vec{F}_{1 \rightarrow 2}=\frac{1}{4\pi\epsilon_0}\frac{q_{1}q_{2}}{(r_{1 \rightarrow 2})^3}\vec{r}_{1 \rightarrow 2}=\frac{1}{4\pi\epsilon_0}\frac{q_{1}q_{2}}{(r_{1 \rightarrow 2})^2}\hat{r}_{1 \rightarrow 2}$$ |
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| Where here we have used the [[184_notes:math_review#Unit_Vectors|definition of the unit vector]] ($\hat{r}=\frac{\vec{r}}{r}$) to get the two different versions of the equation. There are a few things to notice about this equation. First, this equation is **only true for the electric force between two point charges**. Second, this force is **not a constant force** - it depends on the separation distance between the two charges. The closer the two charges are, the stronger the push/pull will be. Finally, this equation may look familiar from mechanics - if you change the charges into masses and change the constant, you will get the equation for [[183_notes:gravitation|Newtonian gravity]] that describes the gravitational interaction between two large masses. It turns out that there are many parallels between the gravitational force and the electric force. | Where here we have used the [[184_notes:math_review#Unit_Vectors|definition of the unit vector]] ($\hat{r}=\frac{\vec{r}}{r}$) to get the two different versions of the equation. There are a few things to notice about this equation. First, this equation is **only true for the electric force between two point charges**. Second, this force is **not a constant force** - it depends on the separation distance between the two charges. **The closer the two charges are, the stronger the push/pull will be.** Finally, this equation may look familiar from mechanics - if you change the charges into masses and change the constant, you will get the equation for [[183_notes:gravitation|Newtonian gravity]] that describes the gravitational interaction between two large masses. It turns out that there are many parallels between the gravitational force and the electric force. |
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| ==== Examples ==== | ==== Examples ==== |
| [[:184_notes:examples:Week3_balloon_wall|Ballon Stuck to a Wall]] | [[:184_notes:examples:Week3_balloon_wall|Ballon Stuck to a Wall]] |