If two negatively charged small sphere, one with twice the charge of the other, are 18cm a part in air. Calculate the charge on each if the force exerted by each on the other is 0.00081?

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