Welcome to Westonci.ca, where you can find answers to all your questions from a community of experienced professionals. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
To solve this problem, you need to apply Coulomb's law, which quantifies the electrostatic force between two point charges. Coulomb's law is given by the formula:
[tex]\[ F = k \cdot \frac{|q_1 \cdot q_2|}{r^2} \][/tex]
where:
- [tex]\( F \)[/tex] is the magnitude of the force between the charges,
- [tex]\( k \)[/tex] is Coulomb's constant, [tex]\( 8.99 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2 \)[/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.
Let's plug in the given values.
1. Convert the charges from microcoulombs (μC) to coulombs (C):
- [tex]\( q_1 = -6 \, \mu C = -6 \times 10^{-6} \, \text{C} \)[/tex]
- [tex]\( q_2 = 3 \, \mu C = 3 \times 10^{-6} \, \text{C} \)[/tex]
2. Substitute the known values into Coulomb's law:
- [tex]\( k = 8.99 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2 \)[/tex]
- [tex]\( r = 0.002 \, \text{m} \)[/tex]
[tex]\[ F = 8.99 \times 10^9 \cdot \frac{|-6 \times 10^{-6} \cdot 3 \times 10^{-6}|}{(0.002)^2} \][/tex]
3. Calculate the product of the charges:
[tex]\[ |-6 \times 10^{-6} \cdot 3 \times 10^{-6}| = 18 \times 10^{-12} \][/tex]
4. Calculate the distance squared:
[tex]\[ (0.002)^2 = 4 \times 10^{-6} \][/tex]
5. Substitute these values into the formula:
[tex]\[ F = 8.99 \times 10^9 \cdot \frac{18 \times 10^{-12}}{4 \times 10^{-6}} \][/tex]
6. Simplify the fraction:
[tex]\[ \frac{18 \times 10^{-12}}{4 \times 10^{-6}} = 4.5 \times 10^{-6} \][/tex]
7. Calculate the final force magnitude:
[tex]\[ F = 8.99 \times 10^9 \cdot 4.5 \times 10^{-6} = 40455 \, \text{N} \][/tex]
The magnitude of the force is approximately [tex]\( 40455 \, \text{N} \)[/tex].
To determine the direction:
- [tex]\( q_1 \)[/tex] is negative.
- [tex]\( q_2 \)[/tex] is positive.
- Since opposite charges attract, the force on [tex]\( q_2 \)[/tex] due to [tex]\( q_1 \)[/tex] will be towards [tex]\( q_1 \)[/tex]. Since [tex]\( q_1 \)[/tex] is north of [tex]\( q_2 \)[/tex], the force on [tex]\( q_2 \)[/tex] will be directed south.
Therefore, the correct answer is:
- Magnitude: [tex]\( 4 \times 10^4 \, \text{N} \)[/tex]
- Direction: South
[tex]\[ F = k \cdot \frac{|q_1 \cdot q_2|}{r^2} \][/tex]
where:
- [tex]\( F \)[/tex] is the magnitude of the force between the charges,
- [tex]\( k \)[/tex] is Coulomb's constant, [tex]\( 8.99 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2 \)[/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.
Let's plug in the given values.
1. Convert the charges from microcoulombs (μC) to coulombs (C):
- [tex]\( q_1 = -6 \, \mu C = -6 \times 10^{-6} \, \text{C} \)[/tex]
- [tex]\( q_2 = 3 \, \mu C = 3 \times 10^{-6} \, \text{C} \)[/tex]
2. Substitute the known values into Coulomb's law:
- [tex]\( k = 8.99 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2 \)[/tex]
- [tex]\( r = 0.002 \, \text{m} \)[/tex]
[tex]\[ F = 8.99 \times 10^9 \cdot \frac{|-6 \times 10^{-6} \cdot 3 \times 10^{-6}|}{(0.002)^2} \][/tex]
3. Calculate the product of the charges:
[tex]\[ |-6 \times 10^{-6} \cdot 3 \times 10^{-6}| = 18 \times 10^{-12} \][/tex]
4. Calculate the distance squared:
[tex]\[ (0.002)^2 = 4 \times 10^{-6} \][/tex]
5. Substitute these values into the formula:
[tex]\[ F = 8.99 \times 10^9 \cdot \frac{18 \times 10^{-12}}{4 \times 10^{-6}} \][/tex]
6. Simplify the fraction:
[tex]\[ \frac{18 \times 10^{-12}}{4 \times 10^{-6}} = 4.5 \times 10^{-6} \][/tex]
7. Calculate the final force magnitude:
[tex]\[ F = 8.99 \times 10^9 \cdot 4.5 \times 10^{-6} = 40455 \, \text{N} \][/tex]
The magnitude of the force is approximately [tex]\( 40455 \, \text{N} \)[/tex].
To determine the direction:
- [tex]\( q_1 \)[/tex] is negative.
- [tex]\( q_2 \)[/tex] is positive.
- Since opposite charges attract, the force on [tex]\( q_2 \)[/tex] due to [tex]\( q_1 \)[/tex] will be towards [tex]\( q_1 \)[/tex]. Since [tex]\( q_1 \)[/tex] is north of [tex]\( q_2 \)[/tex], the force on [tex]\( q_2 \)[/tex] will be directed south.
Therefore, the correct answer is:
- Magnitude: [tex]\( 4 \times 10^4 \, \text{N} \)[/tex]
- Direction: South
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.
