184_notes:examples:week2_electric_potential_negative_point

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184_notes:examples:week2_electric_potential_negative_point [2017/08/28 21:38] – [Example: Electric Potential from a Negatively Charged Balloon] tallpaul184_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 $0 \text{ V}$. Read [[184_notes:superposition#Superposition_of_Electric_Potential|here]] for why this is important.+
  
 ===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*}
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  • Last modified: 2017/08/28 21:38
  • by tallpaul