A small glass bead has been charged to + 30 nC. A tiny ball bearing 1.0 cm above the bead feels a 1.8*10^-2 N downward electric force. What is the charge on the ball bearing?

The charge on the ball bearing = 667 nC or 6.67 * 10⁻⁷ C

Explanation:

Coulombs law: The force of attraction or repulsion between two charges, Q₁ and Q₂, is directly proportional to the product of the charges and inversely proportional to the square of the distance between the two charges

From coulombs law, F = 1/4πε₀ (Q₁Q₂/r²) ... Equation 1

making Q₂ the subject of the equation,

Q₂ = (F*r²) / (Q₁*1/4πε₀) ... Equation 2

Where F = force of attraction, Q₁ = charge of the bead, Q₂ = charge of the ball bearing, r = distance between the bead and the ball bearing.

Given: Q₁ = 30 nC = 30*10⁻⁹ C, F = 1.8*10⁻² N,

r = 1.0 cm = (1/100) = 0.01 m

Constant: 1/4πε₀ = 9*10⁹ Nm²/C²

Substituting these values intto equation 2,

Q₂ = [ (1.8*10⁻²) (0.01) ²]/[ (9*10⁹) (30*10⁻⁹) ]

Q₂ = (1.8*10⁻² * 0.0001) / 270

Q₂ = 6.67 * 10⁻⁷ C. = 667 nC

Therefore the charge on the ball bearing = 667 nC