Two equally charged tiny spheres of mass 1.0 g are placed 2.0 cm apart.When released,they begin to accelerate away from each other at $414 \mathrm {~m} / \mathrm { s } ^ { 2 }$ What is the magnitude of the charge on each sphere,assuming only that the electric force is present? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

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Quizplus · Accepted Answer

The electric force $ F $ can be calculated using $ F = ma $, where $ m = 1.0 \times 10^{-3} $ kg and $ a = 414 $ m/s². Then, using Coulomb's law $ F = \frac{kq^2}{r^2} $, solve for $ q $ with $ r = 0.02 $ m and $ k = 9.0 \times 10^9 $ N∙m²/C². The calculation gives $ q \approx 140 $ nC.

Two Equally Charged Tiny Spheres of Mass 1 414 m/s2414 \mathrm {~m} / \mathrm { s } ^ { 2 }414 m/s2

Two Equally Charged Tiny Spheres of Mass 1 $414 \mathrm {~m} / \mathrm { s } ^ { 2 }$