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184_notes:examples:week3_particle_in_field [2018/05/24 14:58] – curdemma | 184_notes:examples:week3_particle_in_field [2021/05/19 14:30] – schram45 | ||
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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} &&&&&& | ||
Line 22: | Line 22: | ||
\vec{F}=q\vec{E} &&&&&&&& | \vec{F}=q\vec{E} &&&&&&&& | ||
\end{align*} | \end{align*} | ||
+ | |||
+ | ===Assumptions=== | ||
+ | * Point Charge: Allows us to use the electric potential equation, and the problem does not specify anything otherwise. | ||
+ | * Constant charge: Simplifies the value of charge, meaning it is not charging or discharging over time. | ||
+ | * Electric field is constant in accelerator: | ||
+ | * No gravitational effects: Gravity would be another force acting on our charge in this situation, however for simplicity we are not told any mass and neglect gravity for this problem. | ||
+ | * Conservation of energy: No energy is being added or taken out of the system. This means as the charge loses electric potential energy as it leaves the accelerator, | ||
===Representations=== | ===Representations=== | ||
- | {{ 184_notes: | + | [{{ 184_notes: |
===Goal=== | ===Goal=== | ||
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<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 " |
</ | </ | ||