To determine the force acting on object \(A\) due to object \(B\), we can use Coulomb's Law. Coulomb's Law states:
[tex]\[ F = k \frac{|q_1 \cdot q_2|}{r^2} \][/tex]
where:
- \( F \) is the force between the charges,
- \( k \) is the constant of proportionality (Coulomb's constant), \( k = 9.0 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2 \),
- \( q_1 \) and \( q_2 \) are the magnitudes of the charges,
- \( r \) is the distance between the charges.
Given:
- The charge of object \(A\), \( q_A = -0.25 \, \text{C} \),
- The charge of object \(B\), \( q_B = 1 \, \text{C} \),
- The distance between the objects, \( r = 1.5 \, \text{m} \).
First, substitute these values into Coulomb's Law equation:
[tex]\[ F = 9.0 \times 10^9 \frac{|-0.25 \cdot 1|}{1.5^2} \][/tex]
Calculate the magnitude of the force:
[tex]\[ F = 9.0 \times 10^9 \frac{0.25}{2.25} \][/tex]
[tex]\[ F = 9.0 \times 10^9 \times \frac{0.25}{2.25} \][/tex]
[tex]\[ F = 9.0 \times 10^9 \times \frac{1}{9} \][/tex]
[tex]\[ F = 9.0 \times 10^9 \times 0.1111 \][/tex]
[tex]\[ F = 1.0 \times 10^9 \, \text{N} \][/tex]
Since the charges of objects \(A\) and \(B\) are opposite (one negative, one positive), the force between them will be attractive. An attractive force in this context implies that the force on \(A\) is directed towards \(B\), and we traditionally denote attractive forces as negative values.
Thus, the force on object \(A\) is:
[tex]\[ F = -1.0 \times 10^9 \, \text{N} \][/tex]
This matches one of the provided options. Therefore, the correct answer is:
[tex]\[ \boxed{-1.0 \times 10^9 \, \text{N}} \][/tex]
