Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
To calculate the magnitude of the electrical force acting between two charges, we use Coulomb's Law. Coulomb's Law states that the magnitude of the force [tex]\( F \)[/tex] between two point charges is given by the formula:
[tex]\[ F = k \cdot \frac{|q_1 \cdot q_2|}{r^2} \][/tex]
where:
- [tex]\( k \)[/tex] is Coulomb's constant ([tex]\( 8.9875517873681764 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2 \)[/tex]),
- [tex]\( q_1 \)[/tex] and [tex]\( q_2 \)[/tex] are the magnitudes of the charges,
- [tex]\( r \)[/tex] is the distance between the charges.
Given:
- [tex]\( q_1 = 2.4 \times 10^{-8} \, \text{C} \)[/tex]
- [tex]\( q_2 = 1.8 \times 10^{-6} \, \text{C} \)[/tex]
- [tex]\( r = 0.008 \, \text{m} \)[/tex]
Step-by-step solution:
1. Calculate the product of the charges:
[tex]\[ |q_1 \times q_2| = (2.4 \times 10^{-8} \, \text{C}) \times (1.8 \times 10^{-6} \, \text{C}) \][/tex]
[tex]\[ = 4.32 \times 10^{-14} \, \text{C}^2 \][/tex]
2. Square the distance:
[tex]\[ r^2 = (0.008 \, \text{m})^2 \][/tex]
[tex]\[ = 6.4 \times 10^{-5} \, \text{m}^2 \][/tex]
3. Apply Coulomb's Law formula:
[tex]\[ F = \frac{8.9875517873681764 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2 \times 4.32 \times 10^{-14} \, \text{C}^2}{6.4 \times 10^{-5} \, \text{m}^2} \][/tex]
[tex]\[ = 6.0665974564735174 \, \text{N} \][/tex]
4. Round the result to the tenths place:
[tex]\[ F \approx 6.1 \, \text{N} \][/tex]
Therefore, the magnitude of the electrical force acting between the charges is [tex]\( 6.1 \, \text{N} \)[/tex], rounded to the tenths place.
[tex]\[ F = k \cdot \frac{|q_1 \cdot q_2|}{r^2} \][/tex]
where:
- [tex]\( k \)[/tex] is Coulomb's constant ([tex]\( 8.9875517873681764 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2 \)[/tex]),
- [tex]\( q_1 \)[/tex] and [tex]\( q_2 \)[/tex] are the magnitudes of the charges,
- [tex]\( r \)[/tex] is the distance between the charges.
Given:
- [tex]\( q_1 = 2.4 \times 10^{-8} \, \text{C} \)[/tex]
- [tex]\( q_2 = 1.8 \times 10^{-6} \, \text{C} \)[/tex]
- [tex]\( r = 0.008 \, \text{m} \)[/tex]
Step-by-step solution:
1. Calculate the product of the charges:
[tex]\[ |q_1 \times q_2| = (2.4 \times 10^{-8} \, \text{C}) \times (1.8 \times 10^{-6} \, \text{C}) \][/tex]
[tex]\[ = 4.32 \times 10^{-14} \, \text{C}^2 \][/tex]
2. Square the distance:
[tex]\[ r^2 = (0.008 \, \text{m})^2 \][/tex]
[tex]\[ = 6.4 \times 10^{-5} \, \text{m}^2 \][/tex]
3. Apply Coulomb's Law formula:
[tex]\[ F = \frac{8.9875517873681764 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2 \times 4.32 \times 10^{-14} \, \text{C}^2}{6.4 \times 10^{-5} \, \text{m}^2} \][/tex]
[tex]\[ = 6.0665974564735174 \, \text{N} \][/tex]
4. Round the result to the tenths place:
[tex]\[ F \approx 6.1 \, \text{N} \][/tex]
Therefore, the magnitude of the electrical force acting between the charges is [tex]\( 6.1 \, \text{N} \)[/tex], rounded to the tenths place.
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.