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| 184_notes:examples:week2_electric_potential_negative_point [2017/08/28 21:36] – [Example: Electric Potential from a Negatively Charged Balloon] tallpaul | 184_notes:examples:week2_electric_potential_negative_point [2018/05/17 16:49] (current) – curdemma |
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| | [[184_notes:pc_potential|Return to Electric Potential]] |
| ===== Example: Electric Potential from a Negatively Charged Balloon ===== | ===== Example: Electric Potential from a Negatively Charged Balloon ===== |
| Suppose we have a negatively charged balloon with total charge Q=−5.0⋅10−9 C. What is the electric potential at a point P, which is a distance R=20 m from the center of mass of the balloon? A diagram below shows a rough sketch. | Suppose we have a negatively charged balloon with total charge Q=−5.0⋅10−9 C. What is the electric potential (also called voltage) at a point P, which is a distance R=20 m from the center of the balloon? |
| {{ 184_notes:2_potential_positive_balloon.png?150 |Charged Balloon, and Point P}} | |
| |
| ===Facts=== | ===Facts=== |
| * The balloon has total charge Q=−5.0⋅10−9 C. | * The balloon has total charge Q=−5.0⋅10−9 C. |
| * The point P is a distance R=20 m away from the center of mass of the balloon. | * The point P is a distance R=20 m away from the center of the balloon. |
| | * The electric potential due to a point charge can be written as $$V = \frac{1}{4\pi\epsilon_0}\frac{q}{r},$$ where $q$ represents the charge and r is the distance. |
| ===Lacking=== | |
| * The electric potential at $P$. | |
| | |
| ===Approximations & Assumptions=== | |
| * The electric potential at $P$ is due entirely to the balloon. | |
| * $P$ lies outside of the balloon. | |
| * The balloon's electric field outside the balloon acts like a point charge centered at the center of mass of the balloon. | |
| * The electric potential infinitely far away from the balloon is 0 V | |
| |
| ===Representations=== | ===Representations=== |
| * The electric potential due to a point charge (to which we are approximating the balloon) can be written as $$V = \frac{1}{4\pi\epsilon_0}\frac{q}{r},$$ where q represents our charge and r is our distance. | <WRAP TIP> |
| | === Assumption === |
| | We assume P lies outside of the balloon. This is obvious, as $P$ is a distance $R=20 \text{ m}$ away from the center of the balloon. |
| | </WRAP> |
| | [{{ 184_notes:2_potential_positive_balloon.png?150 |Charged Balloon, and Point P}}] |
| | |
| | ===Goal=== |
| | * Find the electric potential at $P$. |
| |
| ====Solution==== | ====Solution==== |
| | <WRAP TIP> |
| | === Approximation === |
| | We approximate the balloon as a point charge. We do this because we have the tools to find the electric potential from a point charge. This seems like a reasonable approximation because the balloon is not too spread out, and we are interested in a point very far from the balloon, so the balloon would "look" like a point charge from the perspective of an observation location that is 20 m away. |
| | </WRAP> |
| | |
| | <WRAP TIP> |
| | === Assumption === |
| | The electric potential infinitely far away from the balloon is 0 V. Read [[184_notes:superposition#Superposition_of_Electric_Potential|here]] for why this is important. |
| | </WRAP> |
| | |
| The electric potential at P is given by | The electric potential at P is given by |
| \begin{align*} | \begin{align*} |