📚 Edexcel Physics: Magnetic Fields Key Points | Edexcel 物理：磁场 考点精讲
Magnetic fields form a core part of the Edexcel A Level Physics specification, bringing together concepts of force, motion, and electromagnetic induction. This article distils the key points you need to master for the exam, from magnetic flux density to transformers, with clear explanations and worked examples.
磁场是 Edexcel A Level 物理考纲中的核心内容，它将力、运动与电磁感应等概念紧密联系在一起。本文梳理了从磁通量密度到变压器等关键考点，配合清晰的解释与示例，帮助你高效备考。
1. Magnetic Fields and Field Lines | 磁场与磁力线
A magnetic field is a region of space where a moving charge or a magnetic material experiences a force. Field lines show the direction a north pole would move: they go from north to south outside a magnet, and south to north inside.
磁场是一块空间区域，运动电荷或磁性材料在其中会受到力的作用。磁力线表示北极受力的方向：在磁体外部从北极指向南极，内部则从南极指向北极。
Field lines never cross. The closer the lines, the stronger the magnetic field. A uniform magnetic field is represented by equally spaced parallel lines, such as between two opposite poles of a horseshoe magnet or inside a solenoid.
磁力线永不相交。力线越密，磁场越强。均匀磁场用力线间距相等的平行线表示，例如蹄形磁铁两极之间或螺线管内部的磁场。
2. Magnetic Flux Density B | 磁通量密度 B
Magnetic flux density, symbol B, is a measure of the strength of a magnetic field. It is defined by the force on a conductor carrying a unit current at right angles to the field. The SI unit is the tesla (T), equivalent to N A⁻¹ m⁻¹.
磁通量密度，符号 B，是衡量磁场强弱的物理量。它由单位电流、单位长度的导体在垂直磁场中所受的力来定义。国际单位是特斯拉 (T)，等价于 N·A⁻¹·m⁻¹。
1 T is a strong field; Earth's magnetic field is about 50 µT. In exam questions, B may be constant (uniform field) or vary with position. Always check the direction of B relative to the current or velocity.
1 T 是一个较强的磁场；地磁场约 50 µT。考试题中，B 可能为常数（均匀场）或随位置变化。解题时务必弄清 B 的方向与电流或速度的夹角关系。
3. Force on a Current-Carrying Conductor | 载流导体受力 (F = BIL sin θ)
A conductor of length L carrying current I in a magnetic field B experiences a magnetic force. The magnitude is given by
长度为 L 的载流导体在磁场 B 中会受到磁力。其大小公式为
F = B I L sin θ
aximum force occurs when the conductor is perpendicular to the field (θ = 90°, sin θ = 1).
其中 θ 是电流方向与磁力线方向的夹角。当导体垂直于磁场时（θ = 90°，sin θ = 1），力达到最大。
The direction of the force is given by Fleming's left-hand rule: thumb – force (motion), forefinger – field (N to S), second finger – current (+ to -). This rule applies to conventional current.
力的方向用弗莱明左手定则判断：拇指——力（运动方向），食指——磁场（N→S），中指——电流（+→-）。该定则适用于常规电流方向。
4. Force on a Moving Charge | 运动电荷受力 (F = qvB sin θ)
For a single charged particle moving with velocity v in a magnetic field B, the force is
对于以速度 v 在磁场 B 中运动的单个带电粒子，受到的力为
F = q v B sin θ
where q is the charge and θ is the angle between v and B. The force is always perpendicular to both v and B, so it does no work and cannot change the particle's speed, only its direction.
其中 q 为电荷量，θ 为 v 与 B 的夹角。力始终垂直于 v 和 B，因此不做功，无法改变速率，只能改变粒子的运动方向。
This relationship explains why a charged particle entering a uniform magnetic field at right angles will follow a circular path. The magnetic force provides the centripetal force:
这解释了为何带电粒子垂直进入均匀磁场后会做圆周运动。磁力提供向心力：
qvB = mv² / r
of curvature r = mv / (qB). This is used in mass spectrometers and particle accelerators.
得出轨道半径 r = mv / (qB)。这被广泛应用于质谱仪和粒子加速器中。
5. Charged Particles in Magnetic Fields | 带电粒子在磁场中的运动
When the velocity is not perpendicular to the field, the particle follows a helical path. The component of velocity parallel to B remains constant, while the perpendicular component causes circular motion.
当速度不完全垂直于磁场时，粒子沿螺旋线路径运动。速度平行于 B 的分量保持不变，垂直分量导致圆周运动，从而合成螺旋运动。
ic force: qE = qvB, so v = E / B. This selects particles of a specific velocity regardless of their mass or charge.
在速度选择器中，利用了正交的电场和磁场。当电场力等于磁力时，粒子无偏转通过：qE = qvB，故 v = E / B。这样便筛选出特定速度的粒子，与质量和电荷无关。
6. Electromagnetic Induction | 电磁感应
Electromagnetic induction is the generation of an e.m.f. (electromotive force) when the magnetic flux through a circuit changes. This can be achieved by moving a magnet near a coil, moving a coil in a magnetic field, or changing the current in an adjacent coil.
电磁感应是指通过电路的磁通量发生变化时产生电动势 (e.m.f.) 的现象。可通过移动磁铁靠近线圈、在磁场中移动线圈，或改变相邻线圈中的电流来实现。
Induced e.m.f. is a result of the magnetic force on free electrons in the conductor. The direction of the induced current is such that it opposes the change causing it (Lenz's law). The magnitude depends on the rate of change of magnetic flux linkage.
感应电动势源于导体中自由电子受到的磁力。感应电流的方向总是试图阻碍引起它的变化（楞次定律）。其大小取决于磁链的变化率。
7. Faraday's Law and Lenz's Law | 法拉第定律与楞次定律
Faraday's law states that the magnitude of the induced e.m.f. is proportional to the rate of change of magnetic flux linkage:
法拉第定律指出，感应电动势的大小正比于磁链的变化率：
ε = -N (ΔΦ / Δt)
where ε is the e.m.f. (V), N is the number of turns, and ΔΦ/Δt is the rate of change of flux per turn (Wb s⁻¹). The negative sign represents Lenz's law.
其中 ε 为电动势 (V)，N 为线圈匝数，ΔΦ/Δt 为每匝磁通量的变化率 (Wb·s⁻¹)。负号体现了楞次定律。
Lenz's law: the direction of the induced current is such that it creates a magnetic field opposing the change in flux. This is a consequence of conservation of energy. If the induced current aided the change, energy would be created from nothing.
楞次定律：感应电流的方向总是使其产生的磁场阻碍原磁通的变化。这是能量守恒的体现。如果感应电流促进变化，就会无中生有产生能量。
8. Magnetic Flux and Flux Linkage | 磁通量与磁链
Magnetic flux Φ through a surface is defined as
穿过某一表面的磁通量 Φ 定义为
Φ = B A cos θ
n the normal to the surface and the magnetic field lines. Unit: weber (Wb). 1 Wb = 1 T m².
其中 A 为表面面积，B 为磁通量密度，θ 为表面法线与磁力线的夹角。单位：韦伯 (Wb)。1 Wb = 1 T·m²。
Magnetic flux linkage NΦ is the product of the number of turns N and the flux per turn. This is the key quantity in Faraday's law. A change in flux linkage, not just flux, induces e.m.f. in a coil.
磁链 NΦ 是线圈匝数 N 与每匝磁通的乘积。这是法拉第定律中的核心量。产生感应电动势的是磁链的变化，而非单纯的磁通变化。
9. Generators and Alternating Current | 发电机与交流电
An a.c. generator (alternator) uses a coil rotating in a uniform magnetic field. The flux linkage varies sinusoidally, inducing an alternating e.m.f.:
交流发电机利用线圈在均匀磁场中旋转。磁链呈正弦变化，产生交变电动势：
ε = ε₀ sin(ωt)
turns, and ω is angular velocity. This e.m.f. drives a current that alternates direction every half-cycle.
其中 ε₀ = BANω，A 为线圈面积，N 为匝数，ω 为角速度。该电动势驱动每半个周期换向一次的交流电流。
The peak voltage and r.m.s. voltage are related by Vr.m.s. = V₀ / √2 oscope traces show the sinusoidal waveform. The period T = 2π / ω and frequency f = 1 / T.
峰值电压与均方根电压满足 Vr.m.s. = V₀ / √2。示波器波形显示正弦波。周期 T = 2π / ω，频率 f = 1 / T。
10. Transformers | 变压器
A transformer changes the magnitude of an alternating voltage. It consists of two coils (primary and secondary) wound on a soft iron core. An alternating current in the primary produces a changing magnetic flux in the core, which links the secondary coil and induces an e.m.f.
变压器用于改变交流电压的大小。它由绕在软铁芯上的两个线圈（初级与次级）组成。初级线圈中的交流电在铁芯中产生交变磁通，耦合到次级线圈并感应出电动势。
For an ideal transformer (100% efficiency, no flux leakage), the voltage ratio equals the turns ratio:
对理想变压器（100% 效率，无漏磁），电压比等于匝数比：
Vs / Vp = Ns / Np
And the power is conserved: Vp Ip = Vs Is. A step-up transformer increases voltage and decreases current; a step-down transformer does the opposite, used for efficient power transmission.
并且功率守恒：Vp Ip = Vs Is。升压变压器提高电压、降低电流；降压变压器则相反，常用于高效输电。
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