To calculate the potential energy of an electron in the Bohr model when moving from infinity to a distance r, one must use the Coulomb potential, which defines the interaction between charged particles. The potential energy can be determined by integrating the electric potential from infinity to the specified distance r. The energy gain during this process is expressed as e multiplied by the change in potential, ΔV. It is important to note that the potential is considered zero at infinity, which simplifies the calculation. Understanding these principles is essential for grasping the foundational concepts in classical electromagnetism and quantum mechanics.