Two identical particles, each with a mass of 10 g and a charge of 2.0 10⁻⁴ C , are held at a separation of 10 cm and subsequently released. Determine the speeds of the particles when the separation becomes large.

Step-by-step solution

Initial potential energy of the system is given by U_i = 1 4 ₀ q^2 r Substituting the given values: U_i = 9 10^9 (2.0 10⁻⁴)^2 0.1 U_i = 9 10^9 4.0 10⁻⁸ 0.1 = 3600 J When the separation becomes very large, the potential energy becomes zero and is entirely converted into the kinetic energy of the two particles. By conservation of mechanical energy: U_i = K_f 3600 = 1 2 mv^2 + 1 2 mv^2 = mv^2 3600 = (10 10⁻³) v^2 v^2 = 3600 10⁻² = 360000 v = 600 m/s