To find the electric force acting between two charges using Coulomb's law, we can follow these steps:
1. Identify the given values:
- Charge [tex]\( q_1 = -0.0050 \)[/tex] Coulombs (C)
- Charge [tex]\( q_2 = 0.0050 \)[/tex] Coulombs (C)
- Distance [tex]\( r = 0.025 \)[/tex] meters (m)
- Coulomb's constant [tex]\( k = 9.00 \times 10^9 \)[/tex] Newton meter squared per Coulomb squared (N·m²/C²)
2. Write down the formula for Coulomb's Law:
[tex]\[
F = \frac{k q_1 q_2}{r^2}
\][/tex]
3. Substitute the given values into the formula:
[tex]\[
F = \frac{(9.00 \times 10^9) \times (-0.0050) \times (0.0050)}{(0.025)^2}
\][/tex]
4. Calculate the denominator:
[tex]\[
(0.025)^2 = 0.000625
\][/tex]
5. Calculate the numerator:
[tex]\[
(9.00 \times 10^9) \times (-0.0050) \times (0.0050) = (9.00 \times 10^9) \times (-0.000025) = -225000000.0
\][/tex]
6. Divide the numerator by the denominator:
[tex]\[
F = \frac{-225000000.0}{0.000625} = -360000000.0 \text{ N}
\][/tex]
7. Take the magnitude for the final choice selections:
The magnitude of the force is:
[tex]\[
|F| = 360000000.0 \text{ N}
\][/tex]
Thus, the correct magnitude answer is:
[tex]\[
\boxed{3.6 \times 10^8 \text{ N}}
\][/tex]
Let's match this with the given choices:
A. [tex]\(-3.6 \times 10^8 \text{ N}\)[/tex]
B. [tex]\(3.6 \times 10^8 \text{ N}\)[/tex]
C. [tex]\(-9.0 \times 10^6 \text{ N}\)[/tex]
D. [tex]\(9.0 \times 10^6 \text{ N}\)[/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{B. \ 3.6 \times 10^8 \text{ N}} \][/tex]
This solution comprehends both the magnitude and the options given, but ensuring the final answer format adheres to positive magnitude considering the options provided.
