IDNLearn.com provides a collaborative environment for finding accurate answers. Join our Q&A platform to access reliable and detailed answers from experts in various fields.
Sagot :
Certainly! Let's solve this step-by-step:
### Given Data:
1. Width of the rectangle [tex]\( \text{width} = 0.15 \, \text{m} \)[/tex]
2. Height of the rectangle [tex]\( \text{height} = 0.05 \, \text{m} \)[/tex]
3. Charge [tex]\( q_1 = -5 \times 10^{-6} \, \text{C} \)[/tex]
4. Charge [tex]\( q_2 = 2 \times 10^{-6} \, \text{C} \)[/tex]
5. Coulomb's constant [tex]\( k = 8.988 \times 10^9 \, \text{N}\cdot\text{m}^2/\text{C}^2 \)[/tex]
### Objective:
Determine the electric potential at the upper right-hand corner of the rectangle.
### Steps to Solve:
1. Distance Calculation:
- The distance from charge [tex]\( q_1 \)[/tex] (located at the upper left-hand corner) to the upper right-hand corner is equal to the width of the rectangle.
[tex]\[ d_1 = 0.15 \, \text{m} \][/tex]
- The distance from charge [tex]\( q_2 \)[/tex] (located at the lower right-hand corner) to the upper right-hand corner can be calculated using the Pythagorean theorem:
[tex]\[ d_2 = \sqrt{(\text{width})^2 + (\text{height})^2} = \sqrt{(0.15)^2 + (0.05)^2} = 0.15811388300841897 \, \text{m} \][/tex]
2. Electric Potential Calculation:
- The electric potential at a point due to a charge is given by:
[tex]\[ V = \frac{k \cdot q}{d} \][/tex]
- Calculate the electric potential at the upper right corner due to [tex]\( q_1 \)[/tex]:
[tex]\[ V_1 = \frac{8.988 \times 10^9 \, \text{N}\cdot\text{m}^2/\text{C}^2 \times (-5 \times 10^{-6} \, \text{C})}{0.15 \, \text{m}} = -299599.99999999994 \, \text{V} \][/tex]
- Calculate the electric potential at the upper right corner due to [tex]\( q_2 \)[/tex]:
[tex]\[ V_2 = \frac{8.988 \times 10^9 \, \text{N}\cdot\text{m}^2/\text{C}^2 \times 2 \times 10^{-6} \, \text{C}}{0.15811388300841897 \, \text{m}} = 113690.20643837357 \, \text{V} \][/tex]
3. Total Electric Potential Calculation:
- The total electric potential at the upper right corner is the algebraic sum of the potentials due to both charges:
[tex]\[ V_{\text{total}} = V_1 + V_2 = -299599.99999999994 \, \text{V} + 113690.20643837357 \, \text{V} = -185909.79356162637 \, \text{V} \][/tex]
### Conclusion:
The electric potential at the upper right-hand corner of the rectangle is [tex]\(-185909.79356162637 \, \text{V}\)[/tex].
### Given Data:
1. Width of the rectangle [tex]\( \text{width} = 0.15 \, \text{m} \)[/tex]
2. Height of the rectangle [tex]\( \text{height} = 0.05 \, \text{m} \)[/tex]
3. Charge [tex]\( q_1 = -5 \times 10^{-6} \, \text{C} \)[/tex]
4. Charge [tex]\( q_2 = 2 \times 10^{-6} \, \text{C} \)[/tex]
5. Coulomb's constant [tex]\( k = 8.988 \times 10^9 \, \text{N}\cdot\text{m}^2/\text{C}^2 \)[/tex]
### Objective:
Determine the electric potential at the upper right-hand corner of the rectangle.
### Steps to Solve:
1. Distance Calculation:
- The distance from charge [tex]\( q_1 \)[/tex] (located at the upper left-hand corner) to the upper right-hand corner is equal to the width of the rectangle.
[tex]\[ d_1 = 0.15 \, \text{m} \][/tex]
- The distance from charge [tex]\( q_2 \)[/tex] (located at the lower right-hand corner) to the upper right-hand corner can be calculated using the Pythagorean theorem:
[tex]\[ d_2 = \sqrt{(\text{width})^2 + (\text{height})^2} = \sqrt{(0.15)^2 + (0.05)^2} = 0.15811388300841897 \, \text{m} \][/tex]
2. Electric Potential Calculation:
- The electric potential at a point due to a charge is given by:
[tex]\[ V = \frac{k \cdot q}{d} \][/tex]
- Calculate the electric potential at the upper right corner due to [tex]\( q_1 \)[/tex]:
[tex]\[ V_1 = \frac{8.988 \times 10^9 \, \text{N}\cdot\text{m}^2/\text{C}^2 \times (-5 \times 10^{-6} \, \text{C})}{0.15 \, \text{m}} = -299599.99999999994 \, \text{V} \][/tex]
- Calculate the electric potential at the upper right corner due to [tex]\( q_2 \)[/tex]:
[tex]\[ V_2 = \frac{8.988 \times 10^9 \, \text{N}\cdot\text{m}^2/\text{C}^2 \times 2 \times 10^{-6} \, \text{C}}{0.15811388300841897 \, \text{m}} = 113690.20643837357 \, \text{V} \][/tex]
3. Total Electric Potential Calculation:
- The total electric potential at the upper right corner is the algebraic sum of the potentials due to both charges:
[tex]\[ V_{\text{total}} = V_1 + V_2 = -299599.99999999994 \, \text{V} + 113690.20643837357 \, \text{V} = -185909.79356162637 \, \text{V} \][/tex]
### Conclusion:
The electric potential at the upper right-hand corner of the rectangle is [tex]\(-185909.79356162637 \, \text{V}\)[/tex].
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. Thank you for visiting IDNLearn.com. We’re here to provide clear and concise answers, so visit us again soon.
