📚 Magnetic Fields and Electromagnetism | 磁场与电磁学
Magnetic fields and electromagnetism form a cornerstone of CIE A-Level Physics, bridging the behaviour of permanent magnets with the dynamic interplay of electricity and magnetism. This article covers key concepts from magnetic flux density and forces on conductors to electromagnetic induction, generators and transformers, equipping you with the essential theory and equations for exam success.
磁场与电磁学是 CIE A-Level 物理的基石内容，将永磁体的行为与电和磁的动态相互作用联系起来。本文涵盖磁通密度、载流导体的受力、电磁感应、发电机与变压器等核心概念，并提供关键理论和方程，助你备考成功。
1. Magnetic Fields and Flux Density | 磁场与磁通密度
A magnetic field is a region in which a force is exerted on a moving charged particle or a magnetic material. Magnetic field lines show the direction of the field: they emerge from north poles and enter south poles. The strength of a magnetic field is measured by the magnetic flux density B, defined as the force per unit current per unit length on a straight conductor placed perpendicular to the field: B = F / (IL). The SI unit is the tesla (T). Magnetic flux Φ is a measure of the total field passing through a given area: Φ = BA cos θ ld lines and the normal to the area. Flux is measured in webers (Wb), where 1 Wb = 1 T m².
磁场是对运动电荷或磁性材料施加力的区域。磁感线显示磁场方向：从北极出发，进入南极。磁场强度用磁通密度 B 衡量，其定义是单位电流每单位长度在垂直于磁场的直导体上所受的力：B = F / (IL)。国际单位是特斯拉 (T)。磁通量 Φ 衡量穿过给定面积的总磁场：Φ = BA cos θ，其中 θ 是磁感线与面积法线之间的夹角。磁通量单位为韦伯 (Wb)，1 Wb = 1 T m²。
2. Magnetic Force on a Current-Carrying Conductor | 载流导体的磁力
When a current-carrying conductor is placed in a magnetic field, it experiences a force. This force is given by F = BIL sin θ r and the magnetic field lines. The direction of the force can be determined using Fleming' epresents the field (from N to S), and the second finger represents the current (from + to – maximum when the conductor is perpendicular to the field (θ = 90°) and zero when parallel.
当载流导体置于磁场中时会受到力的作用。力的大小由 F = BIL sin θ 给出，θ 为导体与磁感线之间的夹角。力的方向可用弗莱明左手定则判断：拇指表示力（推力），食指表示磁场（N 指向 S），中指表示电流（正到负）。当导体与磁场垂直时（θ = 90°）力最大，平行时为零。
3. Lorentz Force on a Moving Charge | 运动电荷的洛伦兹力
A charged particle moving through a magnetic field experiences a force called the Lorentz force. For a particle of charge q moving with velocity v at an angle θ to the field B, the force is F = qvB sin θ. The direction of the force is given by Fleming's left-hand rule but with a slight adaptation: for a positive charge, the second finger points in the direction of motion; for a negative charge, the force direction is reversed. This force is always perpendicular to both velocity and magnetic field, so it does no work and changes only the direction of the particle, not its speed.
带电粒子在磁场中运动时会受到洛伦兹力。对于电荷量为 q 的粒子以速度 v 与磁场 B 成 θ 角运动时，力为 F = qvB sin θ。力的方向可用弗莱明左手定则判断，但需注意：对于正电荷，中指指向运动方向；对于负电荷，力的方向相反。此力始终垂直于速度和磁场，因此不做功，仅改变粒子的运动方向，不改变速率。
4. Circular Motion of Charged Particles | 带电粒子在磁场中的圆周运动
If a charged particle enters a uniform magnetic field perpendicularly, it experiences a constant sideways force, resulting in circular motion. The centripetal force is provided by the Lorentz force: mv²/r = qvB. Thus, the radius of the circular path is r = mv/(qB). The period of revolution T = 2πr/v = 2πm/(qB), which is independent of the particle's speed. This property is exploited in devices such as cyclotrons. When the velocity has a component parallel to the field, the particle follows a helical path.
若带电粒子垂直进入匀强磁场，将受到恒定的侧向力，从而做匀速圆周运动。向心力由洛伦兹力提供：mv²/r = qvB。因此圆轨道半径 r = mv/(qB)。回转周期 T = 2πr/v = 2πm/(qB)，与粒子速率无关。这一特性被用于回旋加速器等装置。当速度有平行于磁场的分量时，粒子会走螺旋路径。
5. Velocity Selector | 速度选择器
A velocity selector uses crossed electric and magnetic fields to select charged particles moving at a specific speed. When particles pass through a region with perpendicular E and B fields, the electric force qE opposes the magnetic force qvB. For particles to travel undeflected, the net force must be zero: qE = qvB, giving v = E/B. Only particles with this speed emerge straight through the slit. This principle is used in mass spectrometers.
速度选择器利用交叉的电场和磁场来筛选特定速度的带电粒子。当粒子穿过具有垂直 E 场和 B 场的区域时，电场力 qE 与磁场力 qvB 方向相反。为使粒子不发生偏转，合力须为零：qE = qvB，由此得到 v = E/B。只有以此速度运动的粒子才能笔直穿过狭缝。这一原理用于质谱仪。
6. Hall Effect | 霍尔效应
The Hall effect arises when a current-carrying conductor is placed in a perpendicular magnetic field, generating a transverse voltage (Hall voltage) across the conductor. Charge carriers are deflected to one side by the Lorentz force, creating a potential difference until the electric force balances the magnetic force. The Hall voltage VH is given by VH = BI/(nqt), where n is the charge carrier density, q is the carrier charge, and t is the thickness of the conductor. The Hall effect can be used to determine the sign of charge carriers and to measure magnetic field strength.
霍尔效应指当载流导体置于垂直磁场中时，在导体横向产生电压（霍尔电压）的现象。载流子在洛伦兹力作用下偏向一侧，形成电势差，直至电场力与磁场力平衡。霍尔电压 VH 可表示为 VH = BI/(nqt)，其中 n 为载流子密度，q 为载流子电荷量，t 为导体厚度。霍尔效应可用于判断载流子类型以及测量磁场强度。
7. Electromagnetic Induction: Flux Linkage | 电磁感应：磁链
Electromagnetic induction occurs when there is a change in magnetic flux linking a circuit. Magnetic flux linkage is defined as the product of the number of turns N in a coil and the flux Φ through each turn: flux linkage = NΦ. The unit is the weber-turn. A change in flux linkage induces an electromotive force (emf). This can be achieved by changing the magnetic field, moving a magnet relative to a coil, or changing the orientation of the coil.
当穿过回路的磁通量发生变化时会发生电磁感应。磁链定义为线圈匝数 N 与每匝磁通量 Φ 的乘积：磁链 = NΦ，单位为韦伯·匝。磁链的变化会感应产生电动势 (emf)。可通过改变磁场、使磁体与线圈相对移动或改变线圈方位来实现磁链变化。
8. Faraday's Law and Lenz's Law | 法拉第定律与楞
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