Final answer:
The free-body diagrams show each charge with electric repulsion and an opposite 3-N force. Using Coulomb's Law, the distance between the charges is determined by solving the formula F = k * |q1 * q2| / r^2, where F is 3 N.
Step-by-step explanation:
The question relates to the application of Coulomb's Law in physics, which defines the magnitude of the electrical force between two point charges. Let's address part (a) and (b) of the question.
For the free-body diagrams, we would illustrate two point charges, marked as +3 µC and +5 µC. Each charge has an arrow pointing away from the other, representing the electric repulsion between like charges. Additionally, there would be arrows of equal length in the opposite direction representing the 3-N forces holding each charge in place.
To find the distance between the charges, we use Coulomb's Law, which is expressed as F = k * |q1 * q2| / r^2, where F is the magnitude of the force between the charges, q1 and q2 are the charges, r is the distance between the centers of the charges, and k is Coulomb's constant (8.987 × 10^9 N*m^2/C^2). Since both charges are provided with equal opposite forces of 3 N to hold them in place, we can set up the equation as 3 N = (8.987 × 10^9 N*m^2/C^2) * (3 × 10^-6 C * 5 × 10^-6 C) / r^2. Solving for r gives us the distance between the charges.