Final answer:
The question involves Physics and Coulomb's law, requiring calculations to determine the charges on two charged spheres based on the measured force and their separation distance.
Step-by-step explanation:
The question pertains to the subject of Physics, specifically the concept of Coulomb's law, which describes the force between two charged objects. We can solve for the charges on the spheres using the formula for Coulomb's law: F = k * |q1 * q2| / r^2, where F is the force between the charges, k is Coulomb's constant (8.99 x 10^9 N·m^2/C^2), q1 and q2 are the magnitudes of the charges, and r is the distance between the centers of the two charges.
To find the charge on the spheres when they're equal, we set q1 = q2 and solve for q. When one sphere has four times the charge of the other, we set q1 = 4q2 or q2 = 4q1 and solve for the charges. In both cases, we use the given force and distance to calculate the charge(s).