To determine 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:
[tex]\[
F = k \frac{|q_1 q_2|}{r^2}
\][/tex]
Where:
- [tex]\( F \)[/tex] is the magnitude of the electrical force.
- [tex]\( k \)[/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 two charges.
- [tex]\( r \)[/tex] is the distance between the charges.
Given data:
- The first charge, [tex]\( q_1 \)[/tex], is [tex]\( 2.4 \times 10^{-8} \, \text{C} \)[/tex].
- The second charge, [tex]\( q_2 \)[/tex], is [tex]\( 1.8 \times 10^{-6} \, \text{C} \)[/tex].
- The distance between the charges, [tex]\( r \)[/tex], is [tex]\( 0.008 \, \text{m} \)[/tex].
Now, plug these values into Coulomb's law formula to compute the force.
[tex]\[
F = 8.99 \times 10^9 \times \frac{(2.4 \times 10^{-8}) \cdot (1.8 \times 10^{-6})}{(0.008)^2}
\][/tex]
First, compute the numerator:
[tex]\[
(2.4 \times 10^{-8}) \cdot (1.8 \times 10^{-6}) = 4.32 \times 10^{-14}
\][/tex]
Next, compute the denominator:
[tex]\[
(0.008)^2 = 6.4 \times 10^{-5}
\][/tex]
Then, divide the numerator by the denominator:
[tex]\[
\frac{4.32 \times 10^{-14}}{6.4 \times 10^{-5}} = 6.75 \times 10^{-10}
\][/tex]
Now, multiply by Coulomb's constant:
[tex]\[
F = 8.99 \times 10^9 \times 6.75 \times 10^{-10} = 6.06825 \, \text{N}
\][/tex]
The exact magnitude of the electrical force is approximately [tex]\( 6.06825 \, \text{N} \)[/tex].
Finally, we round this result to the tenths place:
[tex]\[
F \approx 6.1 \, \text{N}
\][/tex]
Therefore, the magnitude of the electrical force acting between the charges, rounded to the tenths place, is [tex]\( 6.1 \, \text{N} \)[/tex].
