To find the electric force acting between two charges using Coulomb's Law, we can follow these steps:
1. Identify the given values:
- [tex]\( q_1 = -0.0085 \)[/tex] C
- [tex]\( q_2 = -0.0025 \)[/tex] C
- [tex]\( r = 0.0020 \)[/tex] m
- [tex]\( k = 9.00 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2 \)[/tex]
2. Write down Coulomb's Law formula:
[tex]\[
F_e = \frac{k q_1 q_2}{r^2}
\][/tex]
3. Substitute the given values into the formula:
[tex]\[
F_e = \frac{(9.00 \times 10^9) \times (-0.0085) \times (-0.0025)}{(0.0020)^2}
\][/tex]
4. Calculate the denominator:
[tex]\[
(0.0020)^2 = 0.000004 = 4 \times 10^{-6} \, \text{m}^2
\][/tex]
5. Calculate the numerator:
[tex]\[
(9.00 \times 10^9) \times (-0.0085) \times (-0.0025) = (9.00 \times 10^9) \times 0.00002125 = 1.9125 \times 10^8 \, \text{N} \cdot \text{m}^2 / \text{C}^2
\][/tex]
6. Divide the numerator by the denominator:
[tex]\[
F_e = \frac{1.9125 \times 10^8}{4 \times 10^{-6}} = 4.78125 \times 10^{13} \, \text{N}
\][/tex]
Simplified further,
[tex]\[
F_e \approx 4.8 \times 10^{10} \, \text{N}
\][/tex]
So the correct answer is:
A. [tex]\( 4.8 \times 10^{10} \, \text{N} \)[/tex]
