To calculate the electrical force between two point charges, you 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 (\( 8.99 \times 10^9 , \text{N m}^2/\text{C}^2 \)),
- \( q_1 \) and \( q_2 \) are the magnitudes of the charges,
- \( r \) is the distance between the charges.
Given:
- \( q_1 = +6 , \text{C} \)
- \( q_2 = -4 , \text{C} \)
- The distance \( r = 2 , \text{m} \)
Plugging the values into the formula:
\[ F = (8.99 \times 10^9) \frac{|(6)(-4)|}{(2)^2} \]
Calculating the values step by step:
-
Calculate the product of the charges: \[ |q_1 q_2| = |6 \times -4| = 24 , \text{C}^2 \]
-
Calculate \( r^2 \): \[ r^2 = 2^2 = 4 , \text{m}^2 \]
-
Now substitute these values back into the force equation: \[ F = (8.99 \times 10^9) \frac{24}{4} \]
Simplifying inside the fraction: \[ \frac{24}{4} = 6 \]
-
Now calculate \( F \): \[ F = (8.99 \times 10^9) \times 6 \] \[ F = 53.94 \times 10^9 , \text{N} \] \[ F = 5.394 \times 10^{10} , \text{N} \]
Since \( q_1 \) is positive and \( q_2 \) is negative, the force is attractive, which means that we should assign a negative sign to the force:
\[ F = -5.394 \times 10^{10} , \text{N} \]
Thus, rounding to the appropriate number of significant figures, we can express the final answer as approximately:
\[ F \approx -5.4 \times 10^{10} , \text{N} \]
Therefore, the correct answer is:
–5.4 × 10^10 N