Question Detail
Question
Two small spheres, each with an identical charge, are separated by 1.5 m in a large vat of water (dielectric constant K = 80). If each sphere experiences a force of 2 N, what is the magnitude of the charge on each sphere? (Given: k0 = 9.0 × 109 N·m²/C²)
Correct Answer
Option B is the correct answer.
Detailed Explanation
This problem uses Coulomb's Law modified for a dielectric medium: FE = k0 q² / (K r²). Given FE = 2 N, r = 1.5 m, K = 80, and k0 = 9.0 × 109 N·m²/C². Rearranging for q²: q² = FE K r² / k0 = (2 N)(80)(1.5 m)² / (9.0 × 109 N·m²/C²) = 360 C² / (9.0 × 109) = 4 × 10-8 C². Taking the square root, q = 2 × 10-4 C.
Hint
Remember to include the dielectric constant K in the denominator of Coulomb's Law when the medium is not a vacuum, and be careful with calculations involving squares and square roots.