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--- 184_notes:pc_energy [2020/08/17 17:27] – dmcpadden
+++ 184_notes:pc_energy [2024/01/22 22:26] (current) – [Deriving Electric Potential Energy for Two Point Charges] tdeyoung
@@ Line 23: / Line 23: @@
   * The units of electric potential energy are joules (J) just like all the other forms of energy.
-=== Deriving Electric Potential Energy for Two Point Charges ===
+==== Deriving Electric Potential Energy for Two Point Charges ====
 [{{  184_notes:twocharges.png?300|Two charges are initially separated by  $r_i$ . After some time they are separated by  $r_f$ .}}]
-Using the relationship between force and potential energy, we can derive the electric potential energy between two point charges from the electric force. Suppose we have two positive point charges  $q_1$  and  $q_2$ , who are initially separated by a distance r. We will //__assume  $q_1$  is fixed__// and let  $q_2$  move to infinity. Starting with the general relationship:
+Using the relationship between force and potential energy, we can derive the electric potential energy between two point charges from the electric force. Suppose we have two positive point charges  $q_1$  and  $q_2$ , who are initially separated by a distance r. We will //__assume __// $q_1$ //__ is fixed__// and let  $q_2$  move to infinity. Starting with the general relationship:
   $\Delta U_{elec} = U_f-U_i= -\int_i^f\vec{F}_{elec}\bullet d\vec{r}$
 we can plug in the electric force equation for the force from  $q_1$  on  $q_2$  (point charges), and we know that our initial location is  $r_i=r$  and our final location is  $r_f=\infty$ . So we get:
@@ Line 52: / Line 52: @@
 This energy then is the electric potential energy between two point charges  $q_1$  and  $q_2$  that are separated by a distance  $r$ . If  $U$  is positive,  $q_1$  and  $q_2$  have the same sign and if  $U$  is negative,  $q_1$  and  $q_2$  have opposite signs.
-=== Getting from Energy to Force ===
+==== Getting from Energy to Force ====
 We can also use the inverse of energy-force relationship to get the electric force from electric potential energy. If we know what the electric potential energy is in terms of  $r$ , you can calculate the electric force by taking the negative derivative of energy with respect to  $r$ , which will give you the electric force in the  $\hat{r}$  direction. //__This assumes that your electric potential energy equation does not depend on an angle__//. (If your electric potential energy does depend on an angle, then you have to use the [[https://en.wikipedia.org/wiki/Gradient|gradient]].)
  $\vec{F}=-\frac{dU}{dr}\hat{r}$
@@ Line 71: / Line 71: @@
  $\Delta U=q\Delta V$
-**Note that electric potential energy is NOT the same thing as electric potential**. Electric potential energy requires two charges or a charge interacting with potential, whereas electric potential is from a single charge. Electric potential energy has units of joules and electric potential has units of volts. That being said, electric potential is related to electric potential energy. Electric potential tells you about how much energy there could be, without needing to know charges are interacting.
+**Note that electric potential energy is NOT the same thing as electric potential**. Electric potential energy requires two charges or a charge interacting with potential, whereas electric potential is from a single charge. **Electric potential energy has units of //joules// and electric potential has units of //volts//.** That being said, electric potential is related to electric potential energy. Electric potential tells you about how much energy there could be, without needing to know charges are interacting.
 ====Examples====
-[[:184_notes:examples:Week3_particle_in_field|Particle Acceleration through an Electric Field]]
+  * [[:184_notes:examples:Week3_particle_in_field|Particle Acceleration through an Electric Field]]
+    * Video Example: Particle Acceleration through an Electric Field
-[[:184_notes:examples:Week3_spaceship_asteroid|Preventing an Asteroid Collision]]
+  * [[:184_notes:examples:Week3_spaceship_asteroid|Preventing an Asteroid Collision]]
+    * Video Example: Preventing an Asteroid Collision
+{{youtube>_rghROIzNUk?large}}
+{{youtube>vf_b6k3iXeU?large}}