Differences

This shows you the differences between two versions of the page.

--- 184_notes:examples:week2_electric_potential_positive_point [2017/08/28 21:19] – [Solution] tallpaul
+++ 184_notes:examples:week2_electric_potential_positive_point [2018/05/17 16:48] (current) – curdemma
@@ Line 1: / Line 1: @@
-===== Example: Electric Potential from a Positive Point Charge =====
+[[184_notes:pc_potential|Return to Electric Potential]]
-Suppose we have a positively charged balloon with total charge $Q=5\cdot 10^{-7} \text{ C}$. What is the electric potential at a point $P$, which is a distance $R=50 \text{ cm}$ from the center of mass of the balloon? A diagram below shows a rough sketch.
+===== Example: Electric Potential from a Positively Charged Balloon =====
-{{ 184_notes:2_potential_positive_balloon.png?150 |Charged Balloon, and Point P}}
+Suppose we have a positively charged balloon with total charge $Q=5.0\cdot 10^{-9} \text{ C}$. What is the electric potential (also called voltage) at a point $P$, which is a distance $R=50 \text{ cm}$ from the center of the balloon?
 ===Facts===
-  * The balloon has total charge $Q=5\cdot 10^{-7} \text{ C}$.
+  * The balloon has total charge $Q=5.0\cdot 10^{-9} \text{ C}$.
-  * The point $P$ is a distance $R=50 \text{ cm}$ away from the center of mass of the balloon.
+  * The point $P$ is a distance $R=50 \text{ cm}$ 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===
+===Representations===
-  * The electric potential at $P$.
+<WRAP TIP>
+=== Assumption ===
+We assume $P$ lies outside of the balloon. We make this assumption because it was not specified, but this seems to make more sense than $P$ being inside the balloon. This also helps us draw the representation below, which can be used to bolster our approximation later on of the balloon as a point charge.
+</WRAP>
-===Approximations & Assumptions===
+[{{ 184_notes:2_potential_positive_balloon.png?150 |Charged Balloon, and Point P}}]
-  * 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 $0 \text{ V}$.
-===Representations===
+===Goal===
-  * 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.
+  * Find the electric potential at $P$.
 ====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 points outside the balloon. so the balloon might "look" like a point charge from the perspective of an observation location that is little far away.
+</WRAP>
+<WRAP TIP>
+=== Assumption ===
+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.
+</WRAP>
 The electric potential at $P$ is given by
 \begin{align*}
 V &= \frac{1}{4\pi\epsilon_0}\frac{q}{r} \\
-  &= \frac{1}{4\pi\cdot 8.85\cdot 10^{-12} \frac{\text{C}^2}{\text{Nm}^2}}\frac{5\cdot 10^{-7} \text{ C}}{0.5 \text{ m}} \\
+  &= \frac{1}{4\pi\cdot 8.85\cdot 10^{-12} \frac{\text{C}}{\text{Vm}}}\frac{5\cdot 10^{-9} \text{ C}}{0.5 \text{ m}} \\
+  &= 90 \text{ V}
 \end{align*}