To calculate the electrostatic force between two charged objects, we can use Coulomb's Law, which is given by the formula:
\[ F = k \frac{|q_1 q_2|}{r^2} \]
where:
- \( F \) is the magnitude of the force between the charges,
- \( k \) is Coulomb's constant (\( 9.0 \times 10^9 , \text{N m}^2/\text{C}^2 \)),
- \( q_1 \) and \( q_2 \) are the amounts of the charges, and
- \( r \) is the distance between the charges.
Given:
- Charge of Object A, \( q_A = -0.25 , \text{C} \)
- Charge of Object B, \( q_B = 1.0 , \text{C} \)
- Distance \( r = 1.5 , \text{m} \)
First, we will compute the magnitude of the force:
\[ F = k \frac{|q_A \cdot q_B|}{r^2} = 9.0 \times 10^9 \frac{|(-0.25) \cdot (1.0)|}{(1.5)^2} \]
Calculating the denominator:
\[ (1.5)^2 = 2.25 \]
Now substituting into the formula:
\[ F = 9.0 \times 10^9 \frac{0.25}{2.25} \]
Calculating \( \frac{0.25}{2.25} \):
\[ \frac{0.25}{2.25} \approx 0.1111 \]
Now substituting that back into the force equation:
\[ F \approx 9.0 \times 10^9 \times 0.1111 \approx 1.0 \times 10^9 , \text{N} \]
Now we need to take into account the signs of the charges. Object A has a negative charge and Object B has a positive charge, so they attract each other, which means the force on object A will be directed towards object B (and thus will be negative in a conventional sense).
Hence, the force on A will be:
\[ F \approx -1.0 \times 10^9 , \text{N} \]
The correct answer, considering the direction of the force, is:
-1.0 x 10^9 N
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