📚 D.2 Electric and Magnetic Fields | 电场与磁场
Electric and magnetic fields are fundamental to understanding how charges interact, from the forces between subatomic particles to the operation of motors, generators, and particle accelerators. In the IB Physics syllabus, topic D.2 covers electric field concepts, magnetic force on moving charges and current-carrying wires, and extends into HL with electric potential, motion of charged particles in combined fields, and the magnetic fields created by currents. This article provides a clear and structured revision of all key ideas, including the HL extensions, with paired English and Chinese explanations.
电场和磁场是理解电荷相互作用的基础，从亚原子粒子之间的力到电动机、发电机和粒子加速器的工作都离不开它们。在IB物理大纲中，D.2部分涵盖电场概念、运动电荷和载流导线所受的磁力，并延伸到HL内容，包括电势、带电粒子在复合场中的运动以及电流产生的磁场。本文以清晰的结构梳理所有核心知识点（含HL扩展），并提供中英双语对照解释。
1. Introduction to Electric Fields | 电场简介
An electric field is a region of space where a stationary charge experiences an electric force. The direction of the field is defined as the direction of the force on a small positive test charge. Electric field lines start on positive charges and end on negative charges, and their density indicates the field strength. The electric field strength E given by E = F/q, where F is the force on a test charge q. Its SI unit is N C⁻¹ or V m⁻¹.
电场是静止电荷受到电力的空间区域。电场方向定义为小正检验电荷所受力的方向。电场线始于正电荷、终于负电荷，其疏密表示场强大小。某点的电场强度 E 由 E = F/q 给出，其中 F 是检验电荷 q 所受的力。其SI单位是 N C⁻¹ 或 V m⁻¹。
2. Coulomb's Law and Electric Field from Point Charges | 库仑定律与点电荷电场
Coulomb' ². The field is radial, pointing away from a positive charge and toward a negative charge.
库仑定律描述两点电荷间的作用力：F = k q₁q₂ / r²，其中 k = 1/(4πε₀) ≈ 8.99×10⁹ N m² C⁻²。异种电荷相吸，同种电荷相斥。离单一点电荷 Q 距离为 r 处的电场强度为 E = k Q / r²。该电场呈辐射状，正电荷的电场向外，负电荷的电场向内。
Coulomb's law: F = k q₁q₂ / r²
库仑定律：F = k q₁q₂ / r²
3. Uniform Electric Fields | 匀强电场
aced in this field experiences a constant force F = qE, resulting in constant acceleration along the field direction for positive charges.
两块连接到电势差的平行导体板之间会产生匀强电场。电场线平行且等间距。电场强度恒定，由 E = V / d 给出，其中 V 是电势差，d 是板间距。置于此场中的电荷受到恒力 F = qE，正电荷沿电场方向获得恒定加速度。
4. Work, Potential Difference and Electronvolt | 功、电势差与电子伏特
erence of 1 V. 1 eV = 1.60×10⁻¹⁹ J. This concept is essential for particle physics and electronics.
当电荷 q 通过电势差 ΔV 时，电场做功 W = qΔV。如果电荷逆着电场移动，则需要外力做功。电子伏特 (eV) 是一个方便的能量单位：1 eV 是一个电子经过 1 V 电势差后获得的能量。1 eV = 1.60×10⁻¹⁹ J。这一概念在粒子物理和电子学中不可或缺。
5. Introduction to Magnetic Fields | 磁场简介
r a current-carrying conductor of length L, the force is F = BIL sinθ. The direction of the force is determined by Fleming's left-hand rule (for conventional current) or the right-hand palm rule.
磁场是运动电荷受到磁力的区域。磁感线在磁体外从北极指向南极。运动电荷所受的磁力垂直于其速度 v 和磁场 B，由 F = qvB sinθ 给出，其中 θ 是 v 与 B 的夹角。对于长度为 L 的载流导线，磁力为 F = BIL sinθ。力的方向由弗莱明左手定则（针对常规电流）或右手掌定则判定。
6. Forces on Current-Carrying Wires and Motion of Charges | 载流导线受力与电荷运动
dius of the path is r = mv/(qB). The period of circular motion is T = 2πm/(qB), which is independent of speed. These ideas are crucial for understanding devices like the mass spectrometer.
当一根载有电流 I 的直导线垂直于匀强磁场 B 放置时，单位长度的受力为 F/L = BI。这一原理应用在电动机中。对于单个运动电荷，磁力充当向心力，导致圆周运动：qvB = mv²/r，因此轨道半径 r = mv/(qB)。圆周运动的周期 T = 2πm/(qB)，与速度无关。这些概念对于理解质谱仪等设备至关重要。
7. HL: Electric Potential Due to Point Charges | HL：点电荷的电势
q₂ / r. Equipotential surfaces are surfaces on which the potential is constant; they are always perpendicular to electric field lines. Around a point charge, equipotentials are concentric spheres.
距离点电荷 Q 为 r 处的电势 V 是将一个小的正检验电荷从无穷远处移到该点过程中每单位电荷所做的功：V = kQ / r。两个相距为 r 的点电荷 q₁ 与 q₂ 组成的系统具有电势能 U = k q₁ q₂ / r。等势面是电势恒定的曲面，始终与电场线垂直。点电荷周围的等势面为同心球面。
8. HL: Relating Electric Field and Potential | HL：电场与电势的关系
dr. The negative sign indicates that the field points in the direction of decreasing potential. This gradient relationship can be used to calculate E from known potential functions, or to find the potential difference by integrating the field.
在匀强电场中，沿电场方向相距 d 的两点之间的电势差为 ΔV = -E d。E 的大小即为 E = ΔV / Δd。对于径向电场，关系更为普遍：E = -dV/dr。负号表示电场指向电势降低的方向。这一梯度关系可用于从已知电势函数计算 E，或通过积分电场来求电势差。
9. HL: Motion of Charged Particles in Combined Electric and Magnetic Fields | HL：带电粒子在电场与磁场复合场中的运动
y particles with this specific speed pass through undeflected. This device is often coupled with a mass spectrometer, where ions are then deflected by a magnetic field into circular arcs with radius r = mv/(qB). By measuring r, the mass-to-charge ratio can be determined.
当电场 E 和磁场 B 同时作用于运动的带电粒子时，总的洛伦兹力为 F = q(E + v × B)。当电场力与磁力平衡时，粒子沿直线运动。速度选择器利用相互垂直的 E 场和 B 场，使得 qE = qvB，从而 v = E/B。只有具有此特定速度的粒子才能无偏转通过。该装置常与质谱仪联用，随后离子被磁场偏转成半径为 r = mv/(qB) 的圆弧。通过测量 r，可以确定质荷比。
10. HL: Magnetic Fields Produced by Currents | HL：电流产生的磁场
t direction, fingers curl in the direction of the magnetic field. For a solenoid of length L, N turns, and current I, the field inside is approximately uniform and given by B = μ₀ n I, where n = N/L is the number of turns per unit length.
一根载流直导线周围会产生环形磁场。离长直导线距离为 r 处的磁感应强度大小为 B = μ₀ I / (2π r)，其中 μ₀ = 4π×10⁻⁷ T m A⁻¹ 是真空磁导率。方向由右手螺旋定则判断：拇指指向电流方向，弯曲的四指指向磁场方向。对于长度为 L、匝数为 N、电流为 I 的螺线管，其内部的磁场近似均匀，由 B = μ₀ n I 给出，其中 n = N/L 是单位长度的匝数。
11. HL: Force Between Parallel Current-Carrying Wires and the Ampere | HL：平行载流导线间的力与安培定义
ch, when flowing through two infinitely long, straight parallel conductors of negligible cross-section placed 1 metre apart in a vacuum, produces a force of 2×10⁻⁷ N per metre of length between them.
两根平行导线通以同向电流 I₁ 和 I₂ 会相互吸引；若电流反向则相互排斥。它们之间单位长度的受力为 F/L = μ₀ I₁ I₂ / (2π r)，其中 r 是导线间距。这一关系用于定义安培：1 安培是指当两根横截面积可忽略、无限长、平行的直导线在真空中相距 1 米，通以等量恒定电流时，每米长度上产生 2×10⁻⁷ N 的力所需的电流。
F/L = μ₀ I₁ I₂ / (2π r)
12. HL: The Cyclotron and Applications | HL：回旋加速器及其应用
using a perpendicular magnetic field and an alternating electric field between two hollow 'D' tant, allowing resonant acceleration. The maximum kinetic energy depends on the maximum radius of the dees: Eₖ = q²B²R² / (2m).
回旋加速器利用垂直磁场和两个空心 D 形电极之间的交变电场来加速带电粒子。磁场迫使粒子沿圆形轨道运动，其周期 T = 2πm/(qB)。交变电压的频率与这一回旋频率匹配：f = qB/(2πm)。随着粒子获得动能，其轨道半径增大，但周期保持不变，从而实现共振加速。最大动能取决于 D 形盒的最大半径：Eₖ = q²B²R² / (2m)。
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