To calculate the magnitude of the electrical force acting between two charges, we use Coulomb's Law. Coulomb's Law states that the magnitude of the force [tex]\( F \)[/tex] between two point charges is given by the formula:
[tex]\[ F = k \cdot \frac{|q_1 \cdot q_2|}{r^2} \][/tex]
where:
- [tex]\( k \)[/tex] is Coulomb's constant ([tex]\( 8.9875517873681764 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2 \)[/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.
Given:
- [tex]\( q_1 = 2.4 \times 10^{-8} \, \text{C} \)[/tex]
- [tex]\( q_2 = 1.8 \times 10^{-6} \, \text{C} \)[/tex]
- [tex]\( r = 0.008 \, \text{m} \)[/tex]
Step-by-step solution:
1. Calculate the product of the charges:
[tex]\[ |q_1 \times q_2| = (2.4 \times 10^{-8} \, \text{C}) \times (1.8 \times 10^{-6} \, \text{C}) \][/tex]
[tex]\[ = 4.32 \times 10^{-14} \, \text{C}^2 \][/tex]
2. Square the distance:
[tex]\[ r^2 = (0.008 \, \text{m})^2 \][/tex]
[tex]\[ = 6.4 \times 10^{-5} \, \text{m}^2 \][/tex]
3. Apply Coulomb's Law formula:
[tex]\[ F = \frac{8.9875517873681764 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2 \times 4.32 \times 10^{-14} \, \text{C}^2}{6.4 \times 10^{-5} \, \text{m}^2} \][/tex]
[tex]\[ = 6.0665974564735174 \, \text{N} \][/tex]
4. Round the result to the tenths place:
[tex]\[ F \approx 6.1 \, \text{N} \][/tex]
Therefore, the magnitude of the electrical force acting between the charges is [tex]\( 6.1 \, \text{N} \)[/tex], rounded to the tenths place.
