To determine the electromagnetic force [tex]\( F_e \)[/tex] between two particles using Coulomb's law, we follow these steps:
1. Identify the given values:
- Charge of the first particle, [tex]\( q_1 = 2.15 \times 10^{-9} \, \text{C} \)[/tex]
- Charge of the second particle, [tex]\( q_2 = 3.22 \times 10^{-9} \, \text{C} \)[/tex]
- Separation distance, [tex]\( r = 0.015 \, \text{m} \)[/tex]
- Coulomb’s constant, [tex]\( k = 9.00 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2 \)[/tex]
2. Write Coulomb's law equation:
[tex]\[
F_e = \frac{k q_1 q_2}{r^2}
\][/tex]
3. Substitute the given values into the equation:
[tex]\[
F_e = \frac{(9.00 \times 10^9) (2.15 \times 10^{-9}) (3.22 \times 10^{-9})}{(0.015)^2}
\][/tex]
4. Calculate the denominator [tex]\( r^2 \)[/tex]:
[tex]\[
r^2 = (0.015)^2 = 0.000225 \, \text{m}^2
\][/tex]
5. Calculate the numerator [tex]\( k \times q_1 \times q_2 \)[/tex]:
[tex]\[
k \times q_1 \times q_2 = (9.00 \times 10^9) \times (2.15 \times 10^{-9}) \times (3.22 \times 10^{-9})
\][/tex]
6. Perform the multiplication in the numerator:
[tex]\[
(2.15 \times 10^{-9}) \times (3.22 \times 10^{-9}) = 6.913 \times 10^{-18}
\][/tex]
[tex]\[
9.00 \times 10^9 \times 6.913 \times 10^{-18} = 6.2217 \times 10^{-8}
\][/tex]
7. Now, divide the result by the denominator [tex]\( r^2 \)[/tex]:
[tex]\[
F_e = \frac{6.2217 \times 10^{-8}}{0.000225}
\][/tex]
8. Perform the division:
[tex]\[
F_e = 0.00027691999999999994 \, \text{N}
\][/tex]
This value is approximately [tex]\(2.77 \times 10^{-4}\)[/tex] N when rounded appropriately.
Thus, the answer is:
B. [tex]\(2.77 \times 10^{-4}\)[/tex] N
