AS Physics Unit 2 (June 2019) – Essential Formula Derivations | AS物理单元2（2019年6月）必备公式推导

📚 AS Physics Unit 2 (June 2019) – Essential Formula Derivations | AS物理单元2（2019年6月）必备公式推导

The June 2019 AS Physics Unit 2 examination paper required students not only to recall standard equations but also to demonstrate a thorough understanding of their origins. Many questions tested the ability to derive key formulas from first principles, linking concepts in electricity, waves, and quantum physics. This article walks through the essential derivations that underpinned the paper, breaking down each logical step so you can tackle similar challenges with confidence.

2019年6月的AS物理单元2试卷不仅要求学生记住标准公式，更要求对公式的来源有透彻理解。许多题目考查了从基本原理推导核心公式的能力，涵盖电学、波动和量子物理等概念。本文将逐一剖析这些关键推导，拆解每一步逻辑，帮助你从容应对类似问题。

1. Deriving the Resistivity Formula | 电阻率公式的推导

The resistance R of a uniform conductor depends on its geometry. Experimentally, R is found to be proportional to the length L and inversely proportional to the cross-sectional area A. This can be written as R ∝ L / A. By introducing a proportionality constant, the resistivity ρ (which depends only on the material), we obtain the defining equation R = ρ L / A.

均匀导体的电阻R取决于其几何形状。实验发现，R与长度L成正比，与横截面积A成反比，即 R ∝ L / A。引入一个仅与材料有关的比例常数——电阻率ρ，便得到定义式 R = ρ L / A。

ρ = R × A / L

Rearranging to make ρ the subject yields ρ = RA/L, a relationship frequently used to determine the resistivity of a wire from measurements of its resistance, length, and diameter.

移项可得 ρ = RA/L，这一关系常用于通过测量导线的电阻、长度和直径来测定材料的电阻率。

2. Deriving the Drift Velocity Equation | 漂移速度方程的推导

Imagine a metallic conductor with cross-sectional area A, containing n free electrons per unit volume, each carrying charge e. When a voltage is applied, the electrons drift with an average velocity v. In a time interval t, each electron travels a distance v t, so the volume of electrons passing a given point is A v t. The number of electrons in this volume is n A v t, and the total charge Q passing that point is n A v t e.

设想一个横截面积为A的金属导体，每单位体积含n个自由电子，每个电子带电荷e。施加电压后，电子以平均漂移速度v运动。在时间t内，每个电子移动距离v t，因此通过某一定点的电子体积为A v t，其中包含 n A v t 个

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