184_notes:pc_energy

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184_notes:pc_energy [2021/05/26 13:43] – schram45184_notes:pc_energy [2024/01/22 22:26] (current) – [Deriving Electric Potential Energy for Two Point Charges] tdeyoung
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 [{{  184_notes:twocharges.png?300|Two charges are initially separated by $r_i$. After some time they are separated by $r_f$.}}] [{{  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:
  $$\Delta U_{elec} = U_f-U_i= -\int_i^f\vec{F}_{elec}\bullet d\vec{r}$$  $$\Delta U_{elec} = U_f-U_i= -\int_i^f\vec{F}_{elec}\bullet d\vec{r}$$
 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: 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:
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