Final answer:
We apply Coulomb's law to find the product of the charges on two repelling metal spheres, given the total charge and the force. After finding the product of the charges, we solve a system of equations to determine the individual charge on the sphere with the lesser amount.
Step-by-step explanation:
The student asks about the distribution of charge between two metal spheres that exert a repulsive force on each other when they are a certain distance apart. This is a classic physics problem involving Coulomb's law, which relates the electrostatic force between two charges to the product of the charges, the distance between them, and a constant of proportionality. Given that the total charge is 3.80C and the repulsive force is 4.7×10⁴ⁱN when the spheres are 10.00 cm apart, we first use Coulomb's law to find the product of the charges and then solve a system of equations to find the individual charges.
To solve this, we'll set the charges on the spheres as q1 and q2, wherein q1+q2 = 3.80C. Then, we'll use the force and distance to set up the equation based on Coulomb's law: F = k * |q1*q2| / r². Here, k is Coulomb's constant (8.987×59×10⁹ Nm²/C²), and r is the distance between the charges (0.10 m). After calculating q1*q2, we can set up a system of equations and solve for q1 and q2.