Final answer:
To find the distance between two point charges, apply Coulomb's Law, rearrange it to solve for the distance, and substitute the given charge and force values into the equation.
Step-by-step explanation:
The situation described in the question involves the electric force between two point charges. To determine the distance between two point charges when the electric force between them is known, we use Coulomb's Law, which states that the force (F) between two charges (q1 and q2) is proportional to the product of the charges and inversely proportional to the square of the distance (r) between them:
F = k × (q1 × q2) / r²
where k is Coulomb's constant (8.988 × 10^9 N·m²/C²).
In this case, we have two charges (2.0 × 10^-6 C and 4.0 × 10^-6 C) and the electric force (5.6 × 10^-6 N) and we need to find r.
Rearranging Coulomb's Law to solve for r gives:
r = √(k × (q1 × q2) / F)
Substituting the given values:
r = √((8.988 × 10^9 N·m²/C² × (2.0 × 10^-6 C × 4.0 × 10^-6 C)) / 5.6 × 10^-6 N)
After performing the calculation, the distance r can be found.