演示环境（数据为演示用途，非真实数据）

本文针对“电容器+棒”模型，从物理角度和数学角度，并结合Matlab分析软件，对含电容充电式电磁感应问题进行了深入讨论。通过动量定理、电容定义式及能量守恒，从物理角度求解了导体棒运动末状态时的速度v、流过导体棒的电量q和电路中产生的焦耳热Q,只关注最终结果。从数学角度，通过微分方程求解和积分运算，分别讨论了电路中的I-t规律及导体棒运动的v-t规律、流过导体棒的电量q-t规律、回路中产生的焦耳热Q-t规律，并在t→∞时，与物理角度讨论所得结果相互验证，讨论了中间过程的物理规律。数理融合和大中衔接双视域下讨论物理问题，有助于深入认识物理现象和规律的本质，培养跨学科思维，提升解决实际问题的综合能力，满足不同层次学习需求。

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.