📚 Magnetic Fields in IB Physics: Key Concepts | IB 物理：磁场 考点精讲
Magnetic fields play a fundamental role in electromagnetism and appear throughout the IB Physics syllabus, from the simple compass needle to the sophisticated particle accelerator. This article covers the essential examination topics: magnetic force on moving charges and current-carrying wires, circular motion in uniform fields, the operation of a mass spectrometer, electromagnetic induction, and the principles of generators and transformers. Each concept is explained with clarity, emphasising the equations, right-hand rules, and real-world applications that examiners love to test.
磁场在电磁学中扮演着基础角色，贯穿整个 IB 物理课程——从简单的指南针到复杂的粒子加速器。本文涵盖磁场核心考点：运动电荷和载流导体在磁场中的受力、匀强磁场中的圆周运动、质谱仪的工作原理、电磁感应以及发电机与变压器的基本原理。每个概念都配以清晰的解释，重点强调方程、右手定则以及考官常考的实际应用。
1. Magnetic Fields and Field Lines | 磁场与磁场线
A magnetic field is a region of space where a moving charge or a magnetic material experiences a force. It is a vector field, symbol B, measured in tesla (T). Magnetic field lines emerge from the north pole and enter the south pole outside a magnet, forming closed loops.
磁场是运动电荷或磁性材料会受到力的空间区域。它是一个矢量场，符号为 B，单位是特斯拉 (T)。在磁体外部，磁场线从北极出发进入南极，形成闭合回路。
The direction of the magnetic field at any point is the direction of the force on a hypothetical north pole placed there. For a long straight current-carrying wire, the field lines are concentric circles, and the direction is given by the right-hand grip rule: thumb points in the direction of conventional current, fingers curl in the direction of the magnetic field.
磁场中任意点的方向就是放在该点的假想北极所受力的方向。对于一根长直载流导线，磁场线是一系列同心圆，方向由右手螺旋定则确定：拇指指向常规电流方向，四指弯曲方向即为磁场方向。
spaced parallel lines. A common source in the lab is a pair of Helmholtz coils. The Earth' ield is approximately uniform over small regions and has a magnitude of around 5 × 10⁻⁵ T.
匀强磁场由等间距的平行线表示。实验室中常用亥姆霍兹线圈产生匀强磁场。地球磁场在小范围内近似均匀，大小约为 5 × 10⁻⁵ T。
2. Magnetic Force on a Moving Charge | 运动电荷在磁场中的受力
A particle with charge q moving with velocity v in a magnetic field B experiences a magnetic force given by:
F = qvB sinθ
带电量为 q 的粒子以速度 v 在磁场 B 中运动时，会受到磁力作用：
F = qvB sinθ
it moves perpendicular to the field (θ = 90°). The direction of the force is given by the right-hand palm rule for a positive charge: fingers point in the direction of B, thumb in the direction of v, and the palm pushes in the direction of F. For a negative charge, the force direction is reversed.
其中 θ 是速度矢量与磁场矢量之间的夹角。当粒子平行于磁场运动时（θ = 0°或 180°），力为零；当垂直于磁场运动时（θ = 90°），力最大。力的方向由右手掌心定则确定（针对正电荷）：四指指向 B，拇指指向 v，掌心推力的方向即为 F。对于负电荷，力的方向相反。
Since the magnetic force is always perpendicular to both v and B, it does no work on the particle. The kinetic energy and speed of the particle remain constant; only the direction of motion changes. This property is crucial for understanding circular motion in magnetic fields.
由于磁力始终垂直于 v 和 B，因此它对粒子不做功。粒子的动能和速率保持不变，只有运动方向发生改变。这一特性是理解磁场中圆周运动的关键。
3. Circular Motion of Charged Particles | 带电粒子在磁场中的圆周运动
When a charged particle enters a uniform magnetic field perpendicularly, the magnetic force provides the centripetal force, causing the particle to move in a circle:
qvB = mv² / r
当带电粒子垂直进入匀强磁场时，磁力提供向心力，使粒子做圆周运动：
qvB = mv²/r
Rearranging gives the radius of the circular path:
r = mv / (qB)
整理可得圆周运动的半径：
r = mv/(qB)
The period T and frequency f of the motion are independent of speed and radius:
T = 2πm / (qB), f = qB / (2πm)
运动的周期 T 和频率 f 与速度、半径无关：
T = 2πm/(qB), f = qB/(2πm)
This frequency is called the cyclotron frequency. The independence from speed is fundamental to the operation of the cyclotron and mass spectrometer, as it ensures that particles of the same specific charge complete one revolution in exactly the same time regardless of their energy.
该频率被称为回旋频率。频率与速度无关的特性是回旋加速器和质谱仪工作的基础，因为相同比荷的粒子无论能量大小，完成一圈的时间完全相同。
4. Applications: Mass Spectrometer | 应用：质谱仪
A mass spectrometer separates ions according to their mass-to-charge ratio. Ions are first accelerated through a potential difference V, gaining kinetic energy:
½ mv² = qV
质谱仪根据离子的质荷比对其进行分离。离子首先通过电势差 V 加速，获得动能：
½ mv² = qV
micircle of radius r = mv/(qB). Combining the two equations eliminates v, giving the mass:
m = (qB²r²) / (2V)
然后它们进入匀强磁场区域 B，沿半径 r = mv/(qB) 的半圆运动。结合两个方程消去 v，得到质量：
m = (qB²r²)/(2V)
By measuring the radius r at which ions land on a detector, the mass m can be determined. This technique is widely used in chemistry and physics to identify isotopes, analyse molecular structures, and measure atomic masses with high precision. In IB Physics questions, you are often asked to derive m from the given parameters or to compare the radii of different isotopes.
通过测量离子落在探测器上的半径 r，可以确定质量 m。该技术广泛用于化学和物理学中识别同位素、分析分子结构以及高精度测量原子量。在 IB 物理题目中，常要求你根据给定参数推导出 m 或比较不同同位素的半径。
5. Magnetic Force on a Current-Carrying Conductor | 载流导体在磁场中的力
A current-carrying wire in a magnetic field experiences a force because the moving charges inside the wire are subject to the magnetic force. For a straight wire of length L carrying current I at an angle θ to a uniform field B, the magnitude of the force is:
F = BIL sinθ
载流导线在磁场中会受力，因为导线中的运动电荷受到磁力作用。对于长度为 L、载有电流 I、与匀强磁场 B 夹角为 θ 的直导线，力的大小为：
F = BIL sinθ
The direction of the force is found using the right-hand rule: hold your thumb, forefinger, and middle finger mutually perpendicular. If the forefinger points along the field B and the middle finger points along the current I (conventional), then the thumb gives the direction of the force F. This is often called the FBI rule.
力的方向用右手定则确定：拇指、食指和中指互相垂直。若食指指向磁场 B，中指指向常规电流 I，则拇指方向即为力 F 的方向，常称为 FBI 定则。
e θ is the angle between the field and the normal to the plane of the coil. Split-ring commutators reverse the current every half turn to maintain rotation in the same direction.
该力是电动机的基础。放置于磁场中的矩形线圈通以电流后会受到力矩作用而旋转。匝数为 N、面积为 A 的线圈所受的力矩为 τ = NIAB sinθ，其中 θ 是磁场与线圈平面法线之间的夹角。换向器（分瓣环）每半圈改变电流方向，以维持单方向持续旋转。
6. Force between Parallel Current-Carrying Wires | 平行载流导线间的力
Two long, straight parallel wires carrying currents I₁ and I₂ separated by a distance r exert a force on each other. The magnetic field produced by one wire at the location of the other is:
B = μ₀I₁ / (2πr)
两长直平行导线分别载流 I₁ 和 I₂，间距为 r，它们彼此施加力的作用。一根导线在另一根导线处产生的磁场为：
B = μ₀I₁/(2πr)
length on the second wire is then F/L = B I₂ = μ₀I₁I₂/(2πr). The direction of the force is attractive if the currents are in the same direction and repulsive if they are opposite aced one metre apart in a vacuum, would produce a force of 2 × 10⁻⁷ N per metre of length.
则第二根导线单位长度所受的力为 F/L = B I₂ = μ₀I₁I₂/(2πr)。力的方向为：同向电流相互吸引，反向电流相互排斥。这一结果定义了安培：真空中相距一米的无限长、截面可忽略的平行直导线中，通过相等的恒定电流，若导
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