Final answer:
The total charge on the two metal spheres can be determined using Coulomb's Law. By setting up and solving an equation based on the given information, we find that the charge on each sphere is approximately 40 nC.
Step-by-step explanation:
The total charge on the two metal spheres can be determined by applying Coulomb's Law. Coulomb's Law states that the force of repulsion between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Let's denote the charge on the first sphere as Q1 and the charge on the second sphere as Q2. The given information tells us that the distance between the spheres is 50 mm (which is equivalent to 0.05 meters), the force of repulsion is 200 N, and the total charge on the spheres is 40 nC (which is equivalent to 40 × 10^-9 C).
Using Coulomb's Law, we can set up the following equation:
F = k * (Q1 * Q2) / r^2
where F represents the force of repulsion, k represents the electrostatic constant (approximately 9 × 10^9 N·m^2/C^2), and r represents the distance between the spheres.
Plugging in the given values:
200 = (9 × 10^9) * ((40 × 10^-9) * (40 × 10^-9)) / (0.05)^2
Simplifying the equation, we find:
(40 × 10^-9)^2 = (0.05)^2 * 200 / (9 × 10^9)
Calculating further:
(40 × 10^-9)^2 = 0.00005
Therefore, the charge on each sphere is approximately 40 nC.