+e -е -e 8 ст 2 cm Two electrons (-e) are separated by 10 cm, and a proton (+e) is placed on the line connecting the two such that is is 2 cm from one of the electrons (see diagram). Calculate the electric potential energy of the proton. (Give your answer in joules but don't include the units.)
+e -е -e 8 ст 2 cm Two electrons (-e) are separated by 10 cm, and a proton (+e) is placed on the line connecting the two such that is is 2 cm from one of the electrons (see diagram). Calculate the electric potential energy of the proton. (Give your answer in joules but don't include the units.)
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Author:Raymond A. Serway, Chris Vuille
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![# Electric Potential Energy Calculation
## Problem Statement
Two electrons (-e) are separated by 10 cm, and a proton (+e) is placed on the line connecting the two such that it is 2 cm from one of the electrons (see diagram). Calculate the electric potential energy of the proton.
*(Give your answer in joules but don't include the units.)*
### Diagram Description
- The diagram depicts three particles aligned horizontally:
- On the left, an electron (-e) is positioned.
- On the far right, another electron (-e) is situated.
- Between the two electrons, a proton (+e) is placed.
- The distance between the left electron and the proton is 8 cm.
- The distance between the proton and the right electron is 2 cm.
### Diagram
```
-e +e -e
●‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒●‒‒‒‒‒‒‒‒‒‒●
8 cm 2 cm
```
### Input Field
[Answer Input Box]
### Submission Instructions
Click *Save and Submit* to save and submit. Click *Save All Answers* to save all answers.
---
### Additional Information
- **Electron Charge (-e):** The elementary charge of an electron.
- **Proton Charge (+e):** The elementary charge of a proton, equal in magnitude to the electron charge but positive.
Setting up the problem involves calculating the potential energy contributions from both the electron-proton pairs.
1. **Electric Potential Energy Formula:**
\[ U = k_e \frac{q_1 q_2}{r} \]
Where:
- \( k_e \) = Coulomb's constant (\( 8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2 \))
- \( q_1 \) and \( q_2 \) are the charges involved (in this case, ±e)
- \( r \) is the distance between the charges
2. **Calculate potential energy:**
\[ U_1 \text{ (due to proton and left electron)} = k_e \frac{(+e)(-e)}{8 \, \text{cm}} \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F240c2e2e-41dc-444c-bfea-c5009c02e973%2F08533d59-7c6a-4188-a016-e4b6a9d90412%2Fu73osmn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:# Electric Potential Energy Calculation
## Problem Statement
Two electrons (-e) are separated by 10 cm, and a proton (+e) is placed on the line connecting the two such that it is 2 cm from one of the electrons (see diagram). Calculate the electric potential energy of the proton.
*(Give your answer in joules but don't include the units.)*
### Diagram Description
- The diagram depicts three particles aligned horizontally:
- On the left, an electron (-e) is positioned.
- On the far right, another electron (-e) is situated.
- Between the two electrons, a proton (+e) is placed.
- The distance between the left electron and the proton is 8 cm.
- The distance between the proton and the right electron is 2 cm.
### Diagram
```
-e +e -e
●‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒●‒‒‒‒‒‒‒‒‒‒●
8 cm 2 cm
```
### Input Field
[Answer Input Box]
### Submission Instructions
Click *Save and Submit* to save and submit. Click *Save All Answers* to save all answers.
---
### Additional Information
- **Electron Charge (-e):** The elementary charge of an electron.
- **Proton Charge (+e):** The elementary charge of a proton, equal in magnitude to the electron charge but positive.
Setting up the problem involves calculating the potential energy contributions from both the electron-proton pairs.
1. **Electric Potential Energy Formula:**
\[ U = k_e \frac{q_1 q_2}{r} \]
Where:
- \( k_e \) = Coulomb's constant (\( 8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2 \))
- \( q_1 \) and \( q_2 \) are the charges involved (in this case, ±e)
- \( r \) is the distance between the charges
2. **Calculate potential energy:**
\[ U_1 \text{ (due to proton and left electron)} = k_e \frac{(+e)(-e)}{8 \, \text{cm}} \
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