Final answer:
To calculate the distance between two charges with a known force between them, apply Coulomb's Law using the values of the charges, Coulomb's constant, and the force to solve for the distance.
Step-by-step explanation:
To find the distance between two charges when the force between them is known, we need to use Coulomb's Law. The law states:
F = k * |q1 * q2| / r2
Where F is the force between the charges, k is Coulomb's constant (8.9875 x 109 N m2 C-2), q1 and q2 are the charges, and r is the distance between the centers of the two charges.
Given that q1 = 2.6 μC, q2 = -4.7 μC, and the force F = 5.70 N, we can solve for r by rearranging Coulomb's Law:
r = sqrt(k * |q1 * q2| / F)
To handle the microCoulomb units, we can convert them to Coulombs: 1 μC = 1 x 10-6 C. We'd plug the values into the equation:
r = sqrt((8.9875 x 109 N m2 C-2) * (2.6 x 10-6 C * -4.7 x 10-6 C) / 5.70 N)
By calculating the above, we'd find the distance r.