IDNLearn.com makes it easy to get reliable answers from knowledgeable individuals. Ask any question and receive accurate, in-depth responses from our dedicated team of experts.
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].
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. Find clear answers at IDNLearn.com. Thanks for stopping by, and come back for more reliable solutions.
