Question Detail
Question
An electrostatic paint has a 200mm diameter metal sphere at a potential of 25KV that repels paint droplets onto a grounded object. What charge is on the sphere?
Correct Answer
Option C is the correct answer.
Detailed Explanation
For a conducting sphere, the potential V is related to the charge Q and radius R by V = kQ/R, where k = 1/(4πε0) ≈ 9 × 109 Nm2/C2.Given: Diameter = 200 mm = 0.2 m, so Radius R = 0.1 m. Potential V = 25 KV = 25,000 V.Q = V × R / k = (25,000 V × 0.1 m) / (9 × 109 Nm2/C2)Q = 2500 / (9 × 109) CQ ≈ 2.777 × 10-7 C = 0.2777 × 10-6 C = 0.2777 μC.Rounding to three decimal places, Q = 0.278 μC.
Hint
Recall the formula for electric potential of a charged sphere and the value of Coulomb's constant.