Physics
Physics
Problem
A tiny insulating bead of mass carries a charge of . The bead is released from rest at a point that is from a fixed point charge of in vacuum. Ignore all forces except the electrostatic interaction between the two charges. Take the zero of electric potential energy at infinite separation. (a) Determine the electric potential energy of the system at the moment the bead is released. (b) Calculate the kinetic energy of the bead after it has moved very far from the fixed charge (effectively at infinite separation). (c) Find the speed of the bead when it is very far away. (d) Explain, using energy conservation, why your answers to parts (a) and (b) must have opposite signs and how this relates to the nature of the force acting on the bead.Intuitive explanation
The key is recognizing that the bead will accelerate toward the fixed charge due to the attractive Coulomb force, converting electric potential energy into kinetic energy. Since you're told to ignore all other forces and given that potential energy is zero at infinity, you can use energy conservation: the initial electric potential energy (calculated from Coulomb's law) equals the final kinetic energy when the bead reaches any new position. This approach avoids having to integrate the force directly.
Intuitive explanation
The key is recognizing that the bead will accelerate toward the fixed charge due to the attractive Coulomb force, converting electric potential energy into kinetic energy. Since you're told to ignore all other forces and given that potential energy is zero at infinity, you can use energy conservation: the initial electric potential energy (calculated from Coulomb's law) equals the final kinetic energy when the bead reaches any new position. This approach avoids having to integrate the force directly.