To determine the force of interaction between the two metallic balls with charges of 5.0 and 7.0 coulombs respectively, placed 1.2 meters apart, we use Coulomb's law. Coulomb's law is given by:
[tex]\[ F = k \frac{q_1 q_2}{r^2} \][/tex]
Where:
- [tex]\( F \)[/tex] is the force of interaction between the charges,
- [tex]\( k \)[/tex] is Coulomb's constant, [tex]\( 9.0 \times 10^9 \, \text{Nm}^2/\text{C}^2 \)[/tex],
- [tex]\( q_1 \)[/tex] and [tex]\( q_2 \)[/tex] are the magnitudes of the charges, 5.0 C and 7.0 C respectively,
- [tex]\( r \)[/tex] is the distance between the charges, 1.2 meters.
Plugging the values into the formula, we get:
[tex]\[
F = (9.0 \times 10^9) \cdot \frac{(5.0) \cdot (7.0)}{(1.2)^2}
\][/tex]
First, let's calculate the denominator:
[tex]\[
1.2^2 = 1.44
\][/tex]
Next, calculate the numerator:
[tex]\[
5.0 \cdot 7.0 = 35.0
\][/tex]
Now, combining these values:
[tex]\[
F = (9.0 \times 10^9) \cdot \frac{35.0}{1.44}
\][/tex]
Simplify the fraction:
[tex]\[
\frac{35.0}{1.44} \approx 24.31
\][/tex]
Multiplying by Coulomb's constant:
[tex]\[
F = 9.0 \times 10^9 \times 24.31 \approx 218790000000 \, \text{N}
\][/tex]
By considering significant figures and rounding appropriately, the closest match in the provided choices is:
[tex]\[
F \approx 2.2 \times 10^{11} \, \text{N}
\][/tex]
Therefore, the correct answer is:
A. [tex]\( 2.2 \times 10^{11} \)[/tex] newtons
