Final answer:
To calculate the final velocity of two identical point charges when they are very far away from each other, we can use the principle of conservation of mechanical energy. By equating the initial electric potential energy to the final kinetic energy, we can solve for the final velocity. The charges' masses and initial separation are given, allowing us to perform the necessary calculations.
Step-by-step explanation:
To calculate the speed at which two identical +7.05 µC point charges will be moving when they are very far away from each other, we can use the principle of conservation of mechanical energy. Initially, the charges are at rest, so their initial kinetic energy is zero. The only form of energy in the system is the electric potential energy between the charges. As the charges move farther apart, the electric potential energy decreases and is converted into kinetic energy. By setting the initial electric potential energy equal to the final kinetic energy, we can solve for the final velocity.
Given that the charges have a mass of 1.49 mg each, we can convert this mass to kilograms and use the formula for kinetic energy (KE = 0.5mv^2) to find the final velocity. The electric potential energy between the charges can be calculated using the equation U = k*q1*q2/r, where k is the electrostatic constant (9 x 10^9 Nm^2/C^2), q1 and q2 are the charges of each particle, and r is the initial separation between the charges.
Substituting the given values into the equations, we can find the final velocity of the charges when they are very far away from each other.