Answer:
the red sphere has a charge of 9.899 10⁻⁶ C and
the green sphere 0.101 10⁻⁶ C
Explanation:
For this exercise we will use coulomb's law
F = k q₁ q₂ / r²
where they indicate the value of the force F = 2.5 N, the distance between them r = 0.06 m
they also indicate the value of the total load
q₁ + q₂ = 10 10⁻⁶ C
we substitute the values
2.5 = 9 10⁹ q₁ q₂ / 0.06²
2.5 0.06 2/9 10⁹ = q₁ q₂
1 10⁻¹² = q₁ q₂
10 10⁻⁶= q₁ + q₂
we have two equations with two i unknowns, so the system can be solved.
q₁ = 1 10⁻¹² / q₂
we substitute in the other equation
10 10⁻⁶ = 10⁻¹² / q₂ + q₂
let's solve the equation
10 10⁻⁶ q₂ = 10⁻¹² + q₂²
q₂² - 10⁻⁵ q₂ + 10⁻¹² = 0
q₂ = [10⁻⁵ ± √(10⁻¹⁰ - 4 10⁻¹²)] / 2
q₂ = [10⁻⁵ + - 0.9798 10⁻⁵] / 2 = 10⁻⁵ (1 + - 0.9798) / 2
q₂ = 0.9899 10⁻⁵ C
q₂ = 0.0101 10⁻⁵ C
let's find the charge of the other sphere
q₂ = 0.9899 10⁻⁵ C
q₁ = 10⁻⁵ - q₂
q₁ = 10⁻⁵ - 0.9899 10⁻⁵
q₁ = 0.0101 10⁻⁵ C
therefore the red sphere has a charge of 9.899 10⁻⁶ C and
the green sphere 0.101 10⁻⁶ C
