Calculate the magnitude of Q2 in units of nanocoulombs

Question

A positively charged particle Q₁ = +15 nC is held fixed at the origin. A second charge Q₂ of mass m = 9.5 μg is floating a distance d = 25 cm above charge Q₁. The net force on Q₂ is equal to zero. You may assume this system is close to the surface of the Earth. 

Calculate the magnitude of Q2 in units of nanocoulombs

Answer 1

Hi Mike S.,

F = k*( Q₁Q₂ )/ r² gives the magnitude of the electric force that either object exerts on the other.

Since Q₂ is floating above Q₁, Q₁ exerts a force on Q₂ equal to the force of gravity on Q₂ (or the weight of Q₂), which is equal to F = m₂g = 9.5 kg * 9.8 m/s². We can find Q₂:

Q₂ = F*r²/(k*Q₁), with r = 25 cm and Q₁ = 15 nC.

Can you take it from here? Be careful with the dimensions.

I hope this helps, Joe.