Question

Two identical + 9.0 μC point charges are initially 5.0 cm from each other. If they are released at the same instant from rest, how fast will each be moving when they are very far away from each other? Assume they have identical masses of 3.0 mg .

Answer 1

In this case the system consists of two identical charges q1 = q2 = 9.0 x 10^(-6) C

Distance between the charges = r = 5.0 x 10^(-2) mrs

mass = 3.0 x 10^ (-6) Kg

Initially the charge system has only electric potential energy and has zero kinetic energy.

after the charges move very far from each other, the system will have zero PE and has only KE

In view of conservation of energy

Initial Total Mechanical Energy = Final Mechanical Energy

or

Initial PE + Initial KE = Final PE + Final KE

$[kq_{1}q_{2}/r] + 0 = 0 + (2)(0.5)mV^2$

[9.0 x 10^9 nt-m^2/C^2 x 9.0 x 10^(-6) C x 9.0 x 10^(-6) C]} / [5 x 10^(-2) mrs] = 3.0 x 10^(-6) Kg x V^2

V= Sqrt [ { 9.0 x 10^9 nt-m^2/C^2 x 9.0 x 10^(-6) C x 9.0 x 10^(-6) C} / { 5 x 10^(-2) mrs x 3 x 10^(-6) Kg} ]

= 2204 m/s