To solve for the force between two charged objects using Coulomb's law, we can follow these steps:
1. Identify the given values:
- Charge of object \( A \), \( q_1 = 4.0 \times 10^{-6} \, C \)
- Charge of object \( B \), \( q_2 = 2.0 \times 10^{-6} \, C \)
- Distance between the objects, \( r = 0.04 \, m \)
- Coulomb's constant, \( k = 9.0 \times 10^9 \, N \cdot m^2 / C^2 \)
2. Write down Coulomb's law:
[tex]\[
F = k \cdot \frac{q_1 \cdot q_2}{r^2}
\][/tex]
Where:
- \( F \) is the force between the two charges
- \( k \) is Coulomb's constant
- \( q_1 \) and \( q_2 \) are the magnitudes of the two charges
- \( r \) is the distance between the charges
3. Substitute the given values into Coulomb's law:
[tex]\[
F = 9.0 \times 10^9 \, \frac{N \cdot m^2}{C^2} \cdot \frac{(4.0 \times 10^{-6} \, C) \cdot (2.0 \times 10^{-6} \, C)}{(0.04 \, m)^2}
\][/tex]
4. Calculate the product of the charges:
[tex]\[
q_1 \cdot q_2 = (4.0 \times 10^{-6}) \cdot (2.0 \times 10^{-6}) = 8.0 \times 10^{-12} \, C^2
\][/tex]
5. Calculate the square of the distance:
[tex]\[
r^2 = (0.04 \, m)^2 = 0.0016 \, m^2
\][/tex]
6. Combine the values and solve for \( F \):
[tex]\[
F = 9.0 \times 10^9 \, \frac{N \cdot m^2}{C^2} \cdot \frac{8.0 \times 10^{-12} \, C^2}{0.0016 \, m^2}
\][/tex]
7. Divide the product of the charges by the distance squared:
[tex]\[
\frac{8.0 \times 10^{-12} \, C^2}{0.0016 \, m^2} = 5.0 \times 10^{-9} \, C^2 / m^2
\][/tex]
8. Multiply by Coulomb’s constant:
[tex]\[
F = 9.0 \times 10^9 \cdot 5.0 \times 10^{-9} = 45 \, N
\][/tex]
Therefore, the force on \( A \) is \( 45 \, N \). The correct answer is:
[tex]\[ \boxed{45 \, N} \][/tex]
