Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
Certainly! Let's step through the solution to find the electric force exerted between two protons located [tex]\(1.00 \times 10^{-15}\)[/tex] meters apart.
We will use Coulomb's law, which states that the electric force ([tex]\( F \)[/tex]) between two point charges is given by:
[tex]\[ F = k \frac{|q_1 q_2|}{r^2} \][/tex]
Where:
- [tex]\( q_1 \)[/tex] is the charge of the first proton,
- [tex]\( q_2 \)[/tex] is the charge of the second proton,
- [tex]\( r \)[/tex] is the distance between the protons,
- [tex]\( k \)[/tex] is Coulomb's constant ([tex]\(8.99 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2\)[/tex]).
Now, let's plug in the given values:
1. The charge of a proton [tex]\( q = 1.60 \times 10^{-19} \)[/tex] Coulombs.
2. The distance between the protons [tex]\( r = 1.00 \times 10^{-15} \)[/tex] meters.
3. Coulomb's constant [tex]\( k = 8.99 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2 \)[/tex].
Step-by-Step Calculation:
1. Identify the charges:
[tex]\( q_1 = 1.60 \times 10^{-19} \)[/tex] C and [tex]\( q_2 = 1.60 \times 10^{-19} \)[/tex] C.
2. Identify the distance between the charges:
[tex]\( r = 1.00 \times 10^{-15} \)[/tex] meters.
3. Apply Coulomb's law:
[tex]\[ F = k \frac{|q_1 q_2|}{r^2} \][/tex]
4. Plug in the values for [tex]\( q_1, q_2, \)[/tex], and [tex]\( r \)[/tex]:
[tex]\[ F = 8.99 \times 10^9 \frac{(1.60 \times 10^{-19})^2}{(1.00 \times 10^{-15})^2} \][/tex]
5. Compute the squared terms:
[tex]\[ q_1 \times q_2 = (1.60 \times 10^{-19}) \times (1.60 \times 10^{-19}) = 2.56 \times 10^{-38} \, \text{C}^2 \][/tex]
[tex]\[ r^2 = (1.00 \times 10^{-15})^2 = 1.00 \times 10^{-30} \, \text{m}^2 \][/tex]
6. Now, compute the electric force:
[tex]\[ F = 8.99 \times 10^9 \frac{2.56 \times 10^{-38}}{1.00 \times 10^{-30}} \][/tex]
7. Simplify the fraction:
[tex]\[ \frac{2.56 \times 10^{-38}}{1.00 \times 10^{-30}} = 2.56 \times 10^{-8} \][/tex]
8. Multiply by Coulomb's constant:
[tex]\[ F = 8.99 \times 10^9 \times 2.56 \times 10^{-8} \][/tex]
[tex]\[ F = 8.99 \times 2.56 \times 10^1 \][/tex]
[tex]\[ F = 230.14399999999995 \, \text{N} \][/tex]
So, the electric force that the two protons exert on each other is approximately:
[tex]\[ F \approx 230.14 \, \text{N} \][/tex]
Therefore, the electric force between the two protons is [tex]\( \boxed{230.14 \, \text{N}} \)[/tex].
We will use Coulomb's law, which states that the electric force ([tex]\( F \)[/tex]) between two point charges is given by:
[tex]\[ F = k \frac{|q_1 q_2|}{r^2} \][/tex]
Where:
- [tex]\( q_1 \)[/tex] is the charge of the first proton,
- [tex]\( q_2 \)[/tex] is the charge of the second proton,
- [tex]\( r \)[/tex] is the distance between the protons,
- [tex]\( k \)[/tex] is Coulomb's constant ([tex]\(8.99 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2\)[/tex]).
Now, let's plug in the given values:
1. The charge of a proton [tex]\( q = 1.60 \times 10^{-19} \)[/tex] Coulombs.
2. The distance between the protons [tex]\( r = 1.00 \times 10^{-15} \)[/tex] meters.
3. Coulomb's constant [tex]\( k = 8.99 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2 \)[/tex].
Step-by-Step Calculation:
1. Identify the charges:
[tex]\( q_1 = 1.60 \times 10^{-19} \)[/tex] C and [tex]\( q_2 = 1.60 \times 10^{-19} \)[/tex] C.
2. Identify the distance between the charges:
[tex]\( r = 1.00 \times 10^{-15} \)[/tex] meters.
3. Apply Coulomb's law:
[tex]\[ F = k \frac{|q_1 q_2|}{r^2} \][/tex]
4. Plug in the values for [tex]\( q_1, q_2, \)[/tex], and [tex]\( r \)[/tex]:
[tex]\[ F = 8.99 \times 10^9 \frac{(1.60 \times 10^{-19})^2}{(1.00 \times 10^{-15})^2} \][/tex]
5. Compute the squared terms:
[tex]\[ q_1 \times q_2 = (1.60 \times 10^{-19}) \times (1.60 \times 10^{-19}) = 2.56 \times 10^{-38} \, \text{C}^2 \][/tex]
[tex]\[ r^2 = (1.00 \times 10^{-15})^2 = 1.00 \times 10^{-30} \, \text{m}^2 \][/tex]
6. Now, compute the electric force:
[tex]\[ F = 8.99 \times 10^9 \frac{2.56 \times 10^{-38}}{1.00 \times 10^{-30}} \][/tex]
7. Simplify the fraction:
[tex]\[ \frac{2.56 \times 10^{-38}}{1.00 \times 10^{-30}} = 2.56 \times 10^{-8} \][/tex]
8. Multiply by Coulomb's constant:
[tex]\[ F = 8.99 \times 10^9 \times 2.56 \times 10^{-8} \][/tex]
[tex]\[ F = 8.99 \times 2.56 \times 10^1 \][/tex]
[tex]\[ F = 230.14399999999995 \, \text{N} \][/tex]
So, the electric force that the two protons exert on each other is approximately:
[tex]\[ F \approx 230.14 \, \text{N} \][/tex]
Therefore, the electric force between the two protons is [tex]\( \boxed{230.14 \, \text{N}} \)[/tex].
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.
