Final answer:
To find the final speed of two particles with equal mass and charge as they move away from each other due to electrostatic repulsion, conservation of energy is applied. The potential energy at the initial separation distance is equated to the kinetic energy when the particles are infinitely far apart, and the final speed is calculated accordingly.
Step-by-step explanation:
The subject question involves calculating the final speed of two particles with equal mass and charge after they are released from rest and move away from each other due to their electrostatic repulsion. To find the final speed when they are very far apart from one another, we can use the conservation of energy principle. Initially, the potential energy (due to the electric potential between the charges) is at its maximum when the distance between the charges is 6×10⁻¹⁰ meters. This potential energy is completely converted into kinetic energy when the particles have moved a very large distance apart and there is no longer any significant electrostatic force acting between them.
Let q be the charge on each particle and d be the separation distance. Then the initial potential energy (U) can be given by the formula U = k*q*q/d, where k is Coulomb's constant (8.988 × 10⁹ N·m²/C²). Since the particles have equal mass (m) and will move apart with the same speed (v) due to symmetry, the final kinetic energy of each particle is (1/2)mv². By setting the initial potential energy equal to the sum of the final kinetic energies of both particles, we can solve for v.