Answer:
The charge on the ball bearing = 667 nC or 6.67 × 10⁻⁷ C
Step-by-step 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