Welcome to Westonci.ca, your go-to destination for finding answers to all your questions. Join our expert community today! Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
Sure, here is a step-by-step solution to find the value of the charge [tex]\( q_2 \)[/tex] given the conditions:
1. Identify the quantities given:
- Coulomb's constant, [tex]\( k = 8.9875517873681764 \times 10^9 \, \text{N m}^2/\text{C}^2 \)[/tex].
- Charge [tex]\( q_1 = 6.33 \, \mu\text{C} = 6.33 \times 10^{-6} \, \text{C} \)[/tex].
- Force, [tex]\( F = 0.115 \, \text{N} \)[/tex].
- Distance between charges, [tex]\( r = 1.44 \, \text{m} \)[/tex].
2. Use Coulomb's Law:
[tex]\[ F = k \cdot \frac{|q_1 \cdot q_2|}{r^2} \][/tex]
3. Solve for [tex]\( q_2 \)[/tex]:
[tex]\[ q_2 = \frac{F \cdot r^2}{k \cdot |q_1|} \][/tex]
4. Plug in the known values:
[tex]\[ q_2 = \frac{0.115 \, \text{N} \cdot (1.44 \, \text{m})^2}{8.9875517873681764 \times 10^9 \, \text{N m}^2/\text{C}^2 \cdot 6.33 \times 10^{-6} \, \text{C}} \][/tex]
5. Calculate the value:
[tex]\[ q_2 = \frac{0.115 \cdot 2.0736}{8.9875517873681764 \times 10^9 \cdot 6.33 \times 10^{-6}} \][/tex]
6. Simplify the numerator and denominator separately:
[tex]\[ q_2 = \frac{0.238464}{8.9875517873681764 \times 10^9 \cdot 6.33 \times 10^{-6}} \][/tex]
7. Combine the constants:
[tex]\[ q_2 = \frac{0.238464}{5.68821556884036957772 \times 10^4} \][/tex]
8. Perform the division:
[tex]\[ q_2 = 4.191579509743604 \times 10^{-6} \, \text{C} \][/tex]
9. Determine the sign:
Since the force between the charges is attractive, and [tex]\( q_1 \)[/tex] is positive ([tex]\(6.33 \, \mu C\)[/tex]), [tex]\( q_2 \)[/tex] must be negative.
Therefore, the value of [tex]\( q_2 \)[/tex] is:
[tex]\[ -4.191579509743604 \times 10^{-6} \, \text{C} \][/tex]
1. Identify the quantities given:
- Coulomb's constant, [tex]\( k = 8.9875517873681764 \times 10^9 \, \text{N m}^2/\text{C}^2 \)[/tex].
- Charge [tex]\( q_1 = 6.33 \, \mu\text{C} = 6.33 \times 10^{-6} \, \text{C} \)[/tex].
- Force, [tex]\( F = 0.115 \, \text{N} \)[/tex].
- Distance between charges, [tex]\( r = 1.44 \, \text{m} \)[/tex].
2. Use Coulomb's Law:
[tex]\[ F = k \cdot \frac{|q_1 \cdot q_2|}{r^2} \][/tex]
3. Solve for [tex]\( q_2 \)[/tex]:
[tex]\[ q_2 = \frac{F \cdot r^2}{k \cdot |q_1|} \][/tex]
4. Plug in the known values:
[tex]\[ q_2 = \frac{0.115 \, \text{N} \cdot (1.44 \, \text{m})^2}{8.9875517873681764 \times 10^9 \, \text{N m}^2/\text{C}^2 \cdot 6.33 \times 10^{-6} \, \text{C}} \][/tex]
5. Calculate the value:
[tex]\[ q_2 = \frac{0.115 \cdot 2.0736}{8.9875517873681764 \times 10^9 \cdot 6.33 \times 10^{-6}} \][/tex]
6. Simplify the numerator and denominator separately:
[tex]\[ q_2 = \frac{0.238464}{8.9875517873681764 \times 10^9 \cdot 6.33 \times 10^{-6}} \][/tex]
7. Combine the constants:
[tex]\[ q_2 = \frac{0.238464}{5.68821556884036957772 \times 10^4} \][/tex]
8. Perform the division:
[tex]\[ q_2 = 4.191579509743604 \times 10^{-6} \, \text{C} \][/tex]
9. Determine the sign:
Since the force between the charges is attractive, and [tex]\( q_1 \)[/tex] is positive ([tex]\(6.33 \, \mu C\)[/tex]), [tex]\( q_2 \)[/tex] must be negative.
Therefore, the value of [tex]\( q_2 \)[/tex] is:
[tex]\[ -4.191579509743604 \times 10^{-6} \, \text{C} \][/tex]
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.