This paper presents an in-depth discussion on the charging-type electromagnetic induction problem involving a “capacitor + rod” model, analyzed from both physical and mathematical perspectives with the aid of Matlab. By using the momentum theorem, capacitance definition, and energy conservation, the velocity at the end state of the conductor rod's motion, the amount of electricity flowing through the conductor rod, and the Joule heat generated in the circuit were solved from a physical perspective, focusing only on the final result. From a mathematical perspective, the I-t relationship in circuits, the v-t relationship of conductor rod motion, the q-t relationship of electric quantity flowing through the conductor rod, and the Q-t relationship of Joule heating generated in the circuit were discussed through differential equation solving and integration operations. As t approaches infinity, the results obtained from the physical angle discussion were mutually verified, and the physical laws of the intermediate process were discussed. Discussing physics problems from the dual perspectives of integrating mathematics and physics, and bridging the gap between large and medium schools, helps to deepen our understanding of the essence of physical phenomena and laws, cultivate interdisciplinary thinking, enhance our comprehensive ability to solve practical problems, and meet the learning needs of different levels.

Potential energy is an important concept in physics, spanning the high school and undergraduate learning stages. This paper systematically addresses various misconceptions in the study of potential energy. It progressively discusses five issues: the relationship between work and the choice of reference frame, the relationship between the work done by a pair of interacting forces and the choice of reference frame, the selection of reference frames in the definition of conservative forces, the work done by conservative forces and potential energy, and the analysis and reasoning of the symmetry of potential energy. The systematic discussion of the comprehensive understanding of potential energy helps construct a more systematic and profound concept of energy and interaction, cultivates scientific thinking literacy. It is conducive to in-depth study of potential energy and a profound understanding of the essence of physical laws from the perspective of the transition from high school to college.