From beginner to expert, IDNLearn.com has answers for everyone. Join our community to receive prompt and reliable responses to your questions from knowledgeable professionals.
Sagot :
To find the electric force between a positive charge and a negative charge separated by a distance of [tex]\( 10^{-15} \)[/tex] meters using Coulomb's law, we can follow these steps:
1. Identify the Given Values:
- [tex]\( e = 1.6 \times 10^{-19} \, \text{C} \)[/tex] (magnitude of charge of an electron)
- [tex]\( k = 8.99 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2 \)[/tex] (Coulomb's constant)
- [tex]\( r = 10^{-15} \, \text{m} \)[/tex] (distance between charges)
- The charges are [tex]\( q_1 = e \)[/tex] and [tex]\( q_2 = -e \)[/tex] (positive and negative charge)
2. Write Coulomb's Law Formula:
- Coulomb's law states: [tex]\( F = k \frac{|q_1 \cdot q_2|}{r^2} \)[/tex]
3. Substitute the Given Values into the Formula:
- [tex]\( q_1 = 1.6 \times 10^{-19} \, \text{C} \)[/tex]
- [tex]\( q_2 = -1.6 \times 10^{-19} \, \text{C} \)[/tex]
- Absolute value of the product of [tex]\( q_1 \)[/tex] and [tex]\( q_2 \)[/tex] is [tex]\( |q_1 \cdot q_2| = |(1.6 \times 10^{-19}) \cdot (-1.6 \times 10^{-19})| = 2.56 \times 10^{-38} \, \text{C}^2 \)[/tex]
4. Calculate the Force Magnitude:
- Substitute the values into the formula:
[tex]\[ \text{Force magnitude} = F = k \frac{|q_1 \cdot q_2|}{r^2} = 8.99 \times 10^9 \frac{2.56 \times 10^{-38}}{(10^{-15})^2} \][/tex]
- Simplify the denominator:
[tex]\[ (10^{-15})^2 = 10^{-30} \][/tex]
- So the expression becomes:
[tex]\[ F = 8.99 \times 10^9 \times \frac{2.56 \times 10^{-38}}{10^{-30}} \][/tex]
5. Simplify the Exponents and Calculate the Result:
- Simplify the fraction:
[tex]\[ \frac{2.56 \times 10^{-38}}{10^{-30}} = 2.56 \times 10^{-8} \][/tex]
- So the expression becomes:
[tex]\[ F = 8.99 \times 10^9 \times 2.56 \times 10^{-8} = 230.144 \, \text{N} \][/tex]
6. Determine the Nature of the Force:
- Since one charge is positive and one is negative, the force is attractive. This means the force should be directed towards each charge, so the force should be negative.
- Therefore, the force is: [tex]\( F = -230.144 \, \text{N} \)[/tex]
7. Choose the Correct Option:
Given the options:
- 230 N
- [tex]\(-230 \, \text{N}\)[/tex]
- 120 N
- [tex]\(-120 \, \text{N}\)[/tex]
Based on our calculation, the correct choice is [tex]\(-230 \, \text{N}\)[/tex].
1. Identify the Given Values:
- [tex]\( e = 1.6 \times 10^{-19} \, \text{C} \)[/tex] (magnitude of charge of an electron)
- [tex]\( k = 8.99 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2 \)[/tex] (Coulomb's constant)
- [tex]\( r = 10^{-15} \, \text{m} \)[/tex] (distance between charges)
- The charges are [tex]\( q_1 = e \)[/tex] and [tex]\( q_2 = -e \)[/tex] (positive and negative charge)
2. Write Coulomb's Law Formula:
- Coulomb's law states: [tex]\( F = k \frac{|q_1 \cdot q_2|}{r^2} \)[/tex]
3. Substitute the Given Values into the Formula:
- [tex]\( q_1 = 1.6 \times 10^{-19} \, \text{C} \)[/tex]
- [tex]\( q_2 = -1.6 \times 10^{-19} \, \text{C} \)[/tex]
- Absolute value of the product of [tex]\( q_1 \)[/tex] and [tex]\( q_2 \)[/tex] is [tex]\( |q_1 \cdot q_2| = |(1.6 \times 10^{-19}) \cdot (-1.6 \times 10^{-19})| = 2.56 \times 10^{-38} \, \text{C}^2 \)[/tex]
4. Calculate the Force Magnitude:
- Substitute the values into the formula:
[tex]\[ \text{Force magnitude} = F = k \frac{|q_1 \cdot q_2|}{r^2} = 8.99 \times 10^9 \frac{2.56 \times 10^{-38}}{(10^{-15})^2} \][/tex]
- Simplify the denominator:
[tex]\[ (10^{-15})^2 = 10^{-30} \][/tex]
- So the expression becomes:
[tex]\[ F = 8.99 \times 10^9 \times \frac{2.56 \times 10^{-38}}{10^{-30}} \][/tex]
5. Simplify the Exponents and Calculate the Result:
- Simplify the fraction:
[tex]\[ \frac{2.56 \times 10^{-38}}{10^{-30}} = 2.56 \times 10^{-8} \][/tex]
- So the expression becomes:
[tex]\[ F = 8.99 \times 10^9 \times 2.56 \times 10^{-8} = 230.144 \, \text{N} \][/tex]
6. Determine the Nature of the Force:
- Since one charge is positive and one is negative, the force is attractive. This means the force should be directed towards each charge, so the force should be negative.
- Therefore, the force is: [tex]\( F = -230.144 \, \text{N} \)[/tex]
7. Choose the Correct Option:
Given the options:
- 230 N
- [tex]\(-230 \, \text{N}\)[/tex]
- 120 N
- [tex]\(-120 \, \text{N}\)[/tex]
Based on our calculation, the correct choice is [tex]\(-230 \, \text{N}\)[/tex].
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Find clear answers at IDNLearn.com. Thanks for stopping by, and come back for more reliable solutions.
