Answer:
q₂ = 3.81 x 10⁻⁸ C = 38.1 nC
q₁ = 7.63 x 10⁻⁸ C = 76.3 nC
Explanation:
The force between two charges is given by Coulomb's:
F = kq₁q₂/r²
where,
F = Force = 0.00081 N
k = Coulomb's Constant = 9 x 10⁹ Nm²/C²
q₁ = magnitude of 1st charge
q₂ = magnitude of second charge
r = distance between charges = 18 cm = 0.18 m
Therefore,
0.00081 N = (9 x 10⁹ Nm²/C²)q₁q₂/(0.18 m)²
q₁q₂ = (0.00081 N)(0.18 m)²/(9 x 10⁹ Nm²/C²)
q₁q₂ = 2.916 x 10⁻¹⁵ C²
q₁ = 2.916 x 10⁻¹⁵ C²/q₂ --------------- equation (1)
It is given that:
q₁ = 2q₂ --------------- equation (2)
Comparing equation (1) and equation (2):
2q₂ = 2.916 x 10⁻¹⁵ C²/q₂
q₂² = 2.916 x 10⁻¹⁵ C²/2
q₂ = √14.58 x 10⁻¹⁶ C²
q₂ = 3.81 x 10⁻⁸ C = 38.1 nC
using this value in equation (2):
q₁= 2(3.81 x 10⁻⁸ C)
q₁ = 7.63 x 10⁻⁸ C = 76.3 nC
