92 3.00 m 93 +- x 4.00 m Three charges are arranged as shown in the picture. 91 = 1 x 10-3 C, 42 = -3 × 10-3 C and q3 = 4 x 10-3 C. What is the potential energy stored in the charges?
92 3.00 m 93 +- x 4.00 m Three charges are arranged as shown in the picture. 91 = 1 x 10-3 C, 42 = -3 × 10-3 C and q3 = 4 x 10-3 C. What is the potential energy stored in the charges?
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![### Arrangement of Charges and Potential Energy Calculation
**Figure Description:**
The figure depicts three point charges positioned in a two-dimensional coordinate system:
- Charge \( q_1 \) is located at the origin (0,0).
- Charge \( q_2 \) is positioned 3.00 meters above \( q_1 \) along the y-axis.
- Charge \( q_3 \) is positioned 4.00 meters to the right of \( q_1 \) along the x-axis.
The charges are as follows:
- \( q_1 = 1 \times 10^{-3} \, \text{C} \)
- \( q_2 = -3 \times 10^{-3} \, \text{C} \)
- \( q_3 = 4 \times 10^{-3} \, \text{C} \)
*Distances between Charges:*
- Distance between \( q_1 \) and \( q_2 \) is 3.00 meters.
- Distance between \( q_1 \) and \( q_3 \) is 4.00 meters.
- Distance between \( q_2 \) and \( q_3 \) can be calculated using the Pythagorean theorem given they form a right triangle. The distance \( d \) is:
\[
d = \sqrt{(4.00 \, \text{m})^2 + (3.00 \, \text{m})^2} = \sqrt{16.00 \, \text{m}^2 + 9.00 \, \text{m}^2} = \sqrt{25.00 \, \text{m}^2} = 5.00 \, \text{m}
\]
**Question:**
What is the potential energy stored in the charges?
**Explanation of Diagrams and Graphs:**
No graphs or additional diagrams are provided besides the initial schematic.
**Solution Approach:**
To find the potential energy stored, the electrostatic potential energy between each pair of charges should be summed up. The formula for potential energy \( U \) between two point charges \( q_i \) and \( q_j \) separated by a distance \( r_{ij} \) is given by:
\[
U_{ij} = \frac{k q_i q_j}{r_{ij}}
\]
where:
-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fabbe649f-9542-4750-a644-5a898c154717%2F8f75744a-f519-4310-817d-8f08d3b05ace%2F1uom2jm_processed.png&w=3840&q=75)
Transcribed Image Text:### Arrangement of Charges and Potential Energy Calculation
**Figure Description:**
The figure depicts three point charges positioned in a two-dimensional coordinate system:
- Charge \( q_1 \) is located at the origin (0,0).
- Charge \( q_2 \) is positioned 3.00 meters above \( q_1 \) along the y-axis.
- Charge \( q_3 \) is positioned 4.00 meters to the right of \( q_1 \) along the x-axis.
The charges are as follows:
- \( q_1 = 1 \times 10^{-3} \, \text{C} \)
- \( q_2 = -3 \times 10^{-3} \, \text{C} \)
- \( q_3 = 4 \times 10^{-3} \, \text{C} \)
*Distances between Charges:*
- Distance between \( q_1 \) and \( q_2 \) is 3.00 meters.
- Distance between \( q_1 \) and \( q_3 \) is 4.00 meters.
- Distance between \( q_2 \) and \( q_3 \) can be calculated using the Pythagorean theorem given they form a right triangle. The distance \( d \) is:
\[
d = \sqrt{(4.00 \, \text{m})^2 + (3.00 \, \text{m})^2} = \sqrt{16.00 \, \text{m}^2 + 9.00 \, \text{m}^2} = \sqrt{25.00 \, \text{m}^2} = 5.00 \, \text{m}
\]
**Question:**
What is the potential energy stored in the charges?
**Explanation of Diagrams and Graphs:**
No graphs or additional diagrams are provided besides the initial schematic.
**Solution Approach:**
To find the potential energy stored, the electrostatic potential energy between each pair of charges should be summed up. The formula for potential energy \( U \) between two point charges \( q_i \) and \( q_j \) separated by a distance \( r_{ij} \) is given by:
\[
U_{ij} = \frac{k q_i q_j}{r_{ij}}
\]
where:
-
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