To solve this problem, we'll use Coulomb's Law to calculate the distance between the two charged table tennis balls. Coulomb's Law is given by:
[tex]\[ F = k \frac{q_1 q_2}{r^2} \][/tex]
where:
- [tex]\( F \)[/tex] is the force between the charges,
- [tex]\( k \)[/tex] is Coulomb's constant ([tex]\( 9.0 \times 10^9 \)[/tex] N·m²/C²),
- [tex]\( q_1 \)[/tex] and [tex]\( q_2 \)[/tex] are the magnitudes of the charges, and
- [tex]\( r \)[/tex] is the distance between the charges.
Given:
- [tex]\( F = 2.4 \times 10^{-5} \)[/tex] N,
- [tex]\( q_1 = 3.8 \times 10^{-8} \)[/tex] C,
- [tex]\( q_2 = 3.0 \times 10^{-8} \)[/tex] C,
- [tex]\( k = 9.0 \times 10^9 \)[/tex] N·m²/C².
We need to find [tex]\( r \)[/tex]. Rearrange Coulomb's Law formula to solve for [tex]\( r \)[/tex]:
[tex]\[ r^2 = k \frac{q_1 q_2}{F} \][/tex]
[tex]\[ r = \sqrt{ k \frac{q_1 q_2}{F} } \][/tex]
First, calculate [tex]\( r^2 \)[/tex]:
[tex]\[ r^2 = 9.0 \times 10^9 \times \frac{3.8 \times 10^{-8} \times 3.0 \times 10^{-8}}{2.4 \times 10^{-5}} \][/tex]
The intermediate result of the expression inside the square root is approximately:
[tex]\[ r^2 \approx 0.42749999999999994 \][/tex]
Now, take the square root of this result to find [tex]\( r \)[/tex]:
[tex]\[ r \approx \sqrt{0.42749999999999994} \][/tex]
[tex]\[ r \approx 0.6538348415311009 \][/tex]
Therefore, the distance between the two charged table tennis balls is approximately 0.65 meters.
Given the answer choices, the closest value is:
A. 0.11 meters
B. 9 meters
C. 0.45 meters
D. 0.65 meters
Hence, the correct answer is:
D. 0.65 meters
