A-Level OCR Physics: Magnetic Fields Revision Guide | A-Level OCR 物理：磁场考点精讲

📚 A-Level OCR Physics: Magnetic Fields Revision Guide | A-Level OCR 物理：磁场考点精讲

Magnetic fields are a cornerstone of A-Level OCR Physics, appearing in multiple-choice, structured questions, and practical assessments. This guide consolidates key concepts, formulae, and applications—from the force on a current-carrying wire to electromagnetic induction—providing a clear pathway for exam success.

磁场是A-Level OCR物理的核心内容，常见于选择题、计算题和实验题。本文梳理了磁场的关键概念、公式和应用，从载流导线受力到电磁感应，为备考提供清晰指引。

1. Magnetic Fields Basics | 磁场基础

A magnetic field is a region of space where a magnetic force can be felt. It is represented by field lines that point from the north pole to the south pole outside a magnet. The strength of the field is indicated by the density of lines.

磁场是存在磁力的空间区域，用磁感线表示，磁体外部的磁感线从北极指向南极。磁感线越密集，磁场越强。

In a uniform magnetic field, the field lines are parallel and equally spaced. This occurs between the opposite poles of two magnets or inside a long solenoid.

在匀强磁场中，磁感线平行且等间距，常见于一对异名磁极之间或长螺线管内部。

2. Magnetic Flux Density B | 磁通量密度 B

Magnetic flux density B is a measure of the strength of a magnetic field. It is defined as the force per unit current per unit length on a straight conductor placed perpendicular to the field:

磁通量密度 B 是衡量磁场强弱的物理量，定义为垂直于磁场的单位电流、单位长度的直导体所受的力：

B = F/(IL)

The SI unit is the tesla (T), where 1 T = 1 N A⁻¹ m⁻¹. A field of 1 T is very strong; the Earth’s magnetic field is about 50 μT.

单位是特斯拉 (T)，1 T = 1 N A⁻¹ m⁻¹。1 T 的磁场极强；地球磁场约 50 μT。

3. Force on a Current-Carrying Conductor (F = BIL) | 安培力

When a straight conductor of length L carrying current I is placed at an angle θ to a uniform magnetic field B, it experiences a force:

当长度为 L 的直导线载有电流 I，且与匀强磁场 B 夹角为 θ 时，导线受到安培力：

F = BIL sin θ

When the conductor is perpendicular to the field (θ = 90°), sin θ = 1 and the force simplifies to F = BIL. For example, a 0.5 m wire carrying 3 A at 90° to a 0.2 T field experiences F = 0.2 × 3 × 0.5 = 0.3 N.

导线与磁场垂直时，sin θ = 1，安培力简化为 F = BIL。例如 0.5 m 导线通以 3 A 电流，垂直于 0.2 T 磁场，受力 0.3 N。

4. Fleming’s Left-Hand Rule | 左手定则

To determine the direction of the force on a current or a moving positive charge, use the left hand: First finger → Field (N to S), Second finger → Current (+ to –), Thumb → Motion (Force). For a negative charge, reverse the current direction in the rule.

左手定则判断电流或正电荷受力方向：食指——磁场方向（N 到 S），中指——电流方向（+ 到 –），拇指——受力方向。负电荷则需将电流方向反向使用。

This rule is essential for solving diagram-based questions and must be practised with different orientations.

该定则是解答示意类题目的关键，需针对不同空间取向反复练习。

5. Force on a Moving Charge (F = BQv) | 洛伦兹力

A single charge Q moving with velocity v at angle θ to a magnetic field B experiences a force:

运动电荷 Q 以速度 v 与磁场 B 成 θ 角运动时，受洛伦兹力：

F = BQv sin θ

If the charge moves perpendicular to the field (θ = 90°), the force is simply F = BQv. The direction for a positive charge follows the left-hand rule with velocity replacing current.

若电荷运动方向与磁场垂直，力简化为 F = BQv。正电荷受力方向按左手定则，电流方向用速度方向代替。

The magnetic force is always perpendicular to the velocity, so it does no work and cannot change the kinetic energy of the particle.

洛伦兹力始终垂直于速度，因此不做功，不改变粒子的动能。

6. Circular Motion in a Magnetic Field | 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:

带电粒子垂直进入匀强磁场时，洛伦兹力提供向心力：

BQv = mv²/r

Hence the radius of the circular path is:

因此，回转半径为：

r = mv/(BQ)

The period T = 2πm/(BQ) is independent of speed. This is why cyclotrons can use a fixed-frequency alternating voltage to accelerate particles.

周期 T = 2πm/(BQ)，与速度无关，这正是回旋加速器利用固定频率交变电压加速粒子的原因。

If the velocity has a component parallel to the field, the particle moves in a helical path.

若初速度含有平行于磁场的分量，粒子将作螺旋运动。

7. Velocity Selector and Mass Spectrometer | 速度选择器与质谱仪

A velocity selector uses crossed electric and magnetic fields. The electric force qE and magnetic force Bqv balance when:

速度选择器利用正交电场和磁场。当电场力 qE 与洛伦兹力 Bqv 平衡时：

v = E/B

Only particles with this specific speed emerge undeflected. In a mass spectrometer, ions are accelerated, pass through a velocity selector, and are then deflected in a uniform magnetic field. The radius r = mv/(Bq) is measured, giving the mass-to-charge ratio m/q.

只有该速度的粒子能直线通过。质谱仪中，离子经加速后通过速度选择器，再在匀强磁场中偏转，通过测量半径 r = mv/(Bq) 求得质荷比 m/q。

8. The Hall Effect | 霍耳效应

When a current-carrying conductor is placed in a perpendicular magnetic field, charge carriers experience a magnetic force, leading to a build-up of charge on one side. This creates a transverse Hall voltage, VH = Bvd, where v is drift velocity and d is the thickness of the conductor. An alternative expression is VH = (BI)/(nqt), where n is charge carrier density.

载流导体垂直放在磁场中时，载流子受洛伦兹力偏转，在侧面累积电荷，产生横向霍耳电压 VH = Bvd，v 为漂移速度，d 为导体厚度。也可表示为 VH = (BI)/(nqt)，其中 n 为载流子浓度。

This effect is used to determine magnetic field strength or charge carrier concentration in materials.

霍耳效应可用于测量磁场强度或材料的载流子浓度。

9. Magnetic Flux and Flux Linkage | 磁通量与磁链

Magnetic flux Φ through an area A is defined as Φ = BA cos θ, where θ is the angle between the magnetic field and the normal to the area. The unit is the weber (Wb), 1 Wb = 1 T m².

穿过面积 A 的磁通量定义为 Φ = BA cos θ，θ 是磁场与面积法线的夹角。单位是韦伯 (Wb)，1 Wb = 1 T m²。

Flux linkage is the product of the number of turns N and the flux through one turn: NΦ. The rate of change of flux linkage determines induced e.m.f.

磁链定义为匝数 N 与单匝磁通量的乘积：NΦ。磁链的变化率决定了感应电动势。

10. Faraday’s Law of Electromagnetic Induction | 法拉第电磁感应定律

Faraday’s Law states that the magnitude of the induced e.m.f. in a circuit is equal to the rate of change of magnetic flux linkage:

法拉第定律指出，回路中感应电动势的大小等于磁链的变化率：

ε = –N ΔΦ/Δt

The negative sign represents Lenz’s Law. This law is the foundation of generators, transformers, and many electromagnetic devices.

负号体现楞次定律。该定律是发电机、变压器和众多电磁设备的基础。

11. Lenz’s Law and Conservation of Energy | 楞次定律与能量守恒

Lenz’s Law: the direction of the induced e.m.f. is such that it opposes the change in magnetic flux that produced it. This is a direct consequence of energy conservation. For example, when a magnet is pushed into a coil, the induced current creates a magnetic field that repels the magnet, requiring work to be done.

楞次定律：感应电动势的方向总是阻碍引起它的磁通量变化，这是能量守恒的必然结果。例如磁铁插入线圈时，感应电流的磁场排斥磁铁，需要外力做功。

Always use Lenz’s Law to determine polarity when applying Faraday’s Law.

应用法拉第定律时，务必用楞次定律确定感应电动势的极性。

12. Transformers | 变压器

An ideal transformer uses two coils wound on a common iron core. The ratio of secondary to primary voltages equals the turns ratio:

理想变压器利用公共铁芯上的两个线圈。次级与初级电压比等于匝数比：

Vs/Vp = Ns/Np

For 100% efficiency, input power equals output power, so Vp Ip = Vs Is. Transformers can step up or step down AC voltages and are essential for long-distance power transmission.

若效率为100%，输入功率等于输出功率，则 Vp Ip = Vs Is。变压器可升降交流电压，对远距离电力传输至关重要。

Published by TutorHao | Physics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）

A-Level OCR Physics: Magnetic Fields Revision Guide | A-Level OCR 物理：磁场 考点精讲