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| 184_notes:examples:week3_particle_in_field [2018/02/03 21:16] – tallpaul | 184_notes:examples:week3_particle_in_field [2018/05/24 15:02] – [Solution] curdemma | ||
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| =====Example: | =====Example: | ||
| Suppose you have a particle with a mass $m$, charge $Q$, initially at rest in an electric field $\vec{E}=E_0\hat{x}$. The electric field extends for a distance $L$ in the $+\hat{x}$-direction before dropping off abruptly to 0. So, the magnitude of the electric field is exactly $E_0$, and then exactly $0$. There is no in-between. What happens to the particle if $Q>0$? What if $Q<0$? What if $Q=0$? In one of these cases, the particle exits the electric field. What is its velocity when it reaches the region of zero electric field? | Suppose you have a particle with a mass $m$, charge $Q$, initially at rest in an electric field $\vec{E}=E_0\hat{x}$. The electric field extends for a distance $L$ in the $+\hat{x}$-direction before dropping off abruptly to 0. So, the magnitude of the electric field is exactly $E_0$, and then exactly $0$. There is no in-between. What happens to the particle if $Q>0$? What if $Q<0$? What if $Q=0$? In one of these cases, the particle exits the electric field. What is its velocity when it reaches the region of zero electric field? | ||
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| * It has charge $Q$, which can be positive or negative or zero. | * It has charge $Q$, which can be positive or negative or zero. | ||
| * The particle is a distance $L$ from the boundary of the electric field. | * The particle is a distance $L$ from the boundary of the electric field. | ||
| - | * We can write the change in electric potential energy (from an initial location " | + | * We can write the change in electric potential energy (from an initial location "$i$" to a final location "$f$") for a point charge two ways here: |
| \begin{align*} | \begin{align*} | ||
| \Delta U &= -\int_i^f\vec{F}\bullet d\vec{r} &&&&&& | \Delta U &= -\int_i^f\vec{F}\bullet d\vec{r} &&&&&& | ||
| \Delta U &= q\Delta V &&&&&& | \Delta U &= q\Delta V &&&&&& | ||
| \end{align*} | \end{align*} | ||
| - | * We can write the change in electric potential (from an initial location " | + | * We can write the change in electric potential (from an initial location "$i$" to a final location "$f$") as |
| \begin{align*} | \begin{align*} | ||
| \Delta V=-\int_i^f \vec{E}\bullet d\vec{r} &&&&&& | \Delta V=-\int_i^f \vec{E}\bullet d\vec{r} &&&&&& | ||
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| ===Representations=== | ===Representations=== | ||
| - | {{ 184_notes: | + | [{{ 184_notes: |
| ===Goal=== | ===Goal=== | ||
| Line 31: | Line 33: | ||
| <WRAP TIP> | <WRAP TIP> | ||
| === Approximation === | === Approximation === | ||
| - | We will approximate the particle as a point charge. We already know it is a " | + | We will approximate the particle as a //__point charge__//. We already know it is a " |
| </ | </ | ||