Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
To calculate the electrostatic force between two charged water molecules, we use Coulomb's Law. Coulomb's Law describes the electrostatic force between two point charges and is given by the formula:
[tex]\[ F = k_e \frac{|q_1 \cdot q_2|}{r^2} \][/tex]
where:
- [tex]\( F \)[/tex] is the electrostatic force,
- [tex]\( k_e \)[/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 identify and plug in the values:
1. Given charges:
- [tex]\( q_1 = 6.4 \times 10^{-10} \, \text{C} \)[/tex]
- [tex]\( q_2 = 1.6 \times 10^{-10} \, \text{C} \)[/tex]
2. Distance between the charges:
- [tex]\( r = 5 \, \text{mm} = 5 \times 10^{-3} \, \text{m} \)[/tex]
Using Coulomb's Law:
[tex]\[ F = 8.99 \times 10^9 \times \frac{|6.4 \times 10^{-10} \cdot 1.6 \times 10^{-10}|}{(5 \times 10^{-3})^2} \][/tex]
Let's first calculate the numerator:
[tex]\[ |6.4 \times 10^{-10} \cdot 1.6 \times 10^{-10}| = 6.4 \times 1.6 \times 10^{-10} \times 10^{-10} = 10.24 \times 10^{-20} \, \text{C}^2 \][/tex]
Now, calculate the denominator:
[tex]\[ (5 \times 10^{-3})^2 = 25 \times 10^{-6} \, \text{m}^2 \][/tex]
Next, plug these values back into the formula:
[tex]\[ F = 8.99 \times 10^9 \times \frac{10.24 \times 10^{-20}}{25 \times 10^{-6}} \][/tex]
[tex]\[ F = 8.99 \times 10^9 \times \frac{10.24 \times 10^{-20}}{2.5 \times 10^{-5}} \][/tex]
Simplify the fraction:
[tex]\[ \frac{10.24 \times 10^{-20}}{2.5 \times 10^{-5}} = 4.096 \times 10^{-15} \][/tex]
Now, multiply by [tex]\( 8.99 \times 10^9 \)[/tex]:
[tex]\[ F = 8.99 \times 10^9 \times 4.096 \times 10^{-15} \][/tex]
[tex]\[ F = 3.682304 \times 10^{-5} \, \text{N} \][/tex]
Thus, the electrostatic force between the two water molecules is approximately:
[tex]\[ 3.682304 \times 10^{-5} \, \text{N} \][/tex]
[tex]\[ F = k_e \frac{|q_1 \cdot q_2|}{r^2} \][/tex]
where:
- [tex]\( F \)[/tex] is the electrostatic force,
- [tex]\( k_e \)[/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 identify and plug in the values:
1. Given charges:
- [tex]\( q_1 = 6.4 \times 10^{-10} \, \text{C} \)[/tex]
- [tex]\( q_2 = 1.6 \times 10^{-10} \, \text{C} \)[/tex]
2. Distance between the charges:
- [tex]\( r = 5 \, \text{mm} = 5 \times 10^{-3} \, \text{m} \)[/tex]
Using Coulomb's Law:
[tex]\[ F = 8.99 \times 10^9 \times \frac{|6.4 \times 10^{-10} \cdot 1.6 \times 10^{-10}|}{(5 \times 10^{-3})^2} \][/tex]
Let's first calculate the numerator:
[tex]\[ |6.4 \times 10^{-10} \cdot 1.6 \times 10^{-10}| = 6.4 \times 1.6 \times 10^{-10} \times 10^{-10} = 10.24 \times 10^{-20} \, \text{C}^2 \][/tex]
Now, calculate the denominator:
[tex]\[ (5 \times 10^{-3})^2 = 25 \times 10^{-6} \, \text{m}^2 \][/tex]
Next, plug these values back into the formula:
[tex]\[ F = 8.99 \times 10^9 \times \frac{10.24 \times 10^{-20}}{25 \times 10^{-6}} \][/tex]
[tex]\[ F = 8.99 \times 10^9 \times \frac{10.24 \times 10^{-20}}{2.5 \times 10^{-5}} \][/tex]
Simplify the fraction:
[tex]\[ \frac{10.24 \times 10^{-20}}{2.5 \times 10^{-5}} = 4.096 \times 10^{-15} \][/tex]
Now, multiply by [tex]\( 8.99 \times 10^9 \)[/tex]:
[tex]\[ F = 8.99 \times 10^9 \times 4.096 \times 10^{-15} \][/tex]
[tex]\[ F = 3.682304 \times 10^{-5} \, \text{N} \][/tex]
Thus, the electrostatic force between the two water molecules is approximately:
[tex]\[ 3.682304 \times 10^{-5} \, \text{N} \][/tex]
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.