To find the electric force between the two charges, we use Coulomb's Law, which is given by the formula:
[tex]\[
F_e = \frac{k q_1 q_2}{r^2}
\][/tex]
where:
- [tex]\( F_e \)[/tex] is the electric force between the charges,
- [tex]\( k \)[/tex] is Coulomb's constant, [tex]\( 9.00 \times 10^9 \, N \cdot m^2 / C^2 \)[/tex],
- [tex]\( q_1 \)[/tex] is the magnitude of the first charge, [tex]\( 0.0042 \, C \)[/tex],
- [tex]\( q_2 \)[/tex] is the magnitude of the second charge, [tex]\( -0.0050 \, C \)[/tex],
- [tex]\( r \)[/tex] is the distance between the charges, [tex]\( 0.0030 \, m \)[/tex].
### Step-by-Step Solution:
1. Identify the values in the problem:
[tex]\[
k = 9.00 \times 10^9 \, N \cdot m^2 / C^2
\][/tex]
[tex]\[
q_1 = 0.0042 \, C
\][/tex]
[tex]\[
q_2 = -0.0050 \, C
\][/tex]
[tex]\[
r = 0.0030 \, m
\][/tex]
2. Substitute the values into the formula:
[tex]\[
F_e = \frac{(9.00 \times 10^9) \cdot (0.0042) \cdot (-0.0050)}{(0.0030)^2}
\][/tex]
3. Calculate the numerator:
[tex]\[
(9.00 \times 10^9) \cdot (0.0042) \cdot (-0.0050) = 9.00 \times 10^9 \times -2.1 \times 10^{-5}
= -1.89 \times 10^5 \, N \cdot m^2 / C^2
\][/tex]
4. Calculate [tex]\( r^2 \)[/tex]:
[tex]\[
(0.0030 \, m)^2 = 0.000009 \, m^2 = 9 \times 10^{-6} \, m^2
\][/tex]
5. Divide the numerator by the denominator:
[tex]\[
F_e = \frac{-1.89 \times 10^5}{9 \times 10^{-6}} = -2.1 \times 10^{10} \, N
\][/tex]
### Conclusion:
The electric force acting between the two charges is:
[tex]\[
-2.1 \times 10^{10} \, N
\][/tex]
### Answer:
B. [tex]\(-2.1 \times 10^{10} \, N\)[/tex]
