📚 Magnetic Fields | 磁场
Magnetic fields are a cornerstone of the IB Physics syllabus, weaving together electricity, motion, and forces into a rich tapestry of physical principles. This article explores the nature of magnetic fields, their sources, and their interactions with moving charges and current‑carrying conductors. We will uncover the rules that govern field patterns, the quantitative laws that describe magnetic forces, and real‑world applications such as the Hall effect. By the end, you will have a firm grasp of the concepts needed to tackle both paper 1 and paper 2 questions with confidence.
磁场是 IB 物理课程的核心内容之一，它将电学、运动学和力学的知识紧密联系在一起。本文探究磁场的本质、来源，以及它们与运动电荷和载流导体之间的相互作用。我们将揭示支配磁场分布的规律、定量描述磁力的定律，以及霍尔效应等实际应用。学完本文后，你将牢固掌握这些概念，能自信地应对试卷一与试卷二中的相关问题。
1. Magnetic Phenomena and Magnetic Fields | 磁现象与磁场
A magnetic field is a region of space where a moving charge or a magnetic material experiences a force. The field is a vector quantity, and its direction at any point is defined as the direction in which the north pole of a small test compass needle points. Magnetic fields are produced by moving charges (electric currents) and by intrinsic magnetic moments of elementary particles, most notably electrons. Unlike electric fields, which originate from static charges, magnetic fields are fundamentally dynamical—they are generated by charge in motion and act only on charge in motion.
磁场是空间中运动电荷或磁性材料会受到力的区域。磁场是矢量，其方向定义为小磁针北极在该处所指的方向。磁场由运动电荷（电流）和基本粒子（尤其是电子）的内禀磁矩产生。与由静止电荷产生的电场不同，磁场本质上是动态的——它们由运动的电荷产生，并且只对运动的电荷施加作用力。
2. Magnetic Flux Density B | 磁感应强度 B
The strength of a magnetic field is quantified by the magnetic flux density, B, often simply called the magnetic field. It is measured in tesla (T). One tesla is defined as the magnetic flux density that produces a force of 1 newton on a charge of 1 coulomb moving perpendicular to the field at 1 metre per second. In IB Physics, we often describe B by the line density of magnetic field lines: the closer the lines, the stronger the field. The vector B is tangent to the field line at any point.
磁场的强弱用磁感应强度 B 来定量描述，通常简称为磁场，单位是特斯拉（T）。1 特斯拉被定义为：1 库仑的电荷以 1 米/秒的速度垂直于磁场方向运动时，受到的力为 1 牛顿。在 IB 物理中，我们常用磁感线的疏密来描述 B 的大小：线越密，场越强。矢量 B 的方向沿磁感线在该点的切线。
3. Magnetic Field Lines | 磁感线
Magnetic field lines are a visual tool used to represent the direction and strength of a magnetic field. They always form closed loops, originating from the north pole and entering the south pole outside a magnet, and continuing from south to north inside the magnet. The lines never intersect. The density of lines is proportional to the magnitude of B. For a uniform magnetic field, such as the interior of a horseshoe magnet or the central region of a long solenoid, the field lines are parallel, equally spaced straight lines.
磁感线是一种直观表示磁场方向和强弱的工具。它们总是形成闭合回路：在磁体外从北极出发指向南极，在磁体内由南极指向北极。磁感线永不相交，其疏密程度与 B 的大小成正比。对于匀强磁场，比如蹄形磁铁内部或长直螺线管的中心区域，磁感线是相互平行、等间距的直线。
4. Magnetic Effect of Electric Currents | 电流的磁效应
Hans Christian Oersted discovered in 1820 that an electric current produces a magnetic field. For a straight, current‑carrying wire, the field lines are concentric circles centred on the wire, and the direction is given by the right‑hand grip rule: if the thumb points in the direction of conventional current, the curled fingers show the direction of the magnetic field. This revelation unified electricity and magnetism and paved the way for electromagnets.
1820 年，汉斯·克里斯蒂安·奥斯特发现电流能够产生磁场。对于长直载流导线，其周围的磁感线是以导线为圆心的同心圆，方向由右手螺旋定则确定：拇指指向电流方向，四指弯曲的方向就是磁场方向。这一发现将电与磁统一起来，为电磁铁的研究铺平了道路。
5. Magnetic Field of a Long Straight Wire | 长直导线的磁场
The magnitude of the magnetic field at a distance r from a long, straight wire carrying a current I is given by the equation:
B = μ₀ I / (2π r)
rmula assumes an infinitely long wire and is accurate for distances small compared to the wire length. The field decreases inversely with distance, and its direction follows the right‑hand grip rule.
距离无限长直导线 r 处的磁感应强度由公式 B = μ₀ I / (2π r) 给出，其中 μ₀ 是真空磁导率，等于 4π × 10⁻⁷ T m A⁻¹。该公式适用于导线长度远大于距离的情况。磁场强度随距离成反比衰减，方向遵循右手螺旋定则。
6. Magnetic Field of a Solenoid | 螺线管的磁场
A solenoid is a long coil of wire consisting of many turns. Inside an ideal solenoid, the magnetic field is uniform and parallel to the axis. The magnitude is:
B = μ₀ n I
t length (n = N / L). The direction of the field inside the solenoid is given by the right‑ le, i.e., the field direction inside the solenoid. The field outside an ideal solenoid is essentially zero.
螺线管是由许多匝线圈组成的细长线圈。在理想螺线管内部，磁场是匀强磁场且平行于轴线。其大小由 B = μ₀ n I 给出，其中 n 是单位长度上的匝数（n = N / L）。螺线管内部的磁场方向同样由右手螺旋定则确定：四指沿电流方向握住螺线管，拇指所指即为 N 极，即管内磁场的方向。理想螺线管外部的磁场几乎为零。
7. Magnetic Flux Φ | 磁通量 Φ
Magnetic flux is a measure of the amount of magnetic field passing through a given area. For a uniform magnetic field B passing through a flat surface of area A, the flux Φ is:
Φ = B A cos θ
ximum; when they are parallel to the surface, the flux is zero. Magnetic flux is a scalar quantity.
磁通量衡量穿过某面积的磁场总量。对于穿过平面面积为 A 的匀强磁场 B，磁通量 Φ = B A cos θ，其中 θ 是磁场方向与面积法线之间的夹角。磁通量的国际单位是韦伯（Wb），1 Wb = 1 T m²。当磁感线垂直于表面时，cos θ = 1，磁通量最大；当磁感线与表面平行时，磁通量为零。磁通量是一个标量。
8. Force on a Moving Charge in a Magnetic Field | 运动电荷在磁场中的力
A charge q moving with velocity v in a magnetic field B experiences a magnetic force F given by the Lorentz force law:
F = q v B sin θ
where θ is the angle between v and B. The direction of F is given by the right‑hand palm rule (for positive charges): fingers point in the direction of B, thumb in the direction of v, and the force comes out of the palm. For a negative charge, the force direction is reversed. This force is always perpendicular to both v and B, so it does no work—it changes only the direction of the velocity, not its magnitude.
以速度 v 在磁场 B 中运动的电荷 q 会受到洛伦兹力 F = q v B sin θ，其中 θ 是 v 与 B 之间的夹角。对于正电荷，力的方向由右手掌定则确定：四指指向 B 的方向，拇指指向 v 的方向，掌心向外则 F 的方向从掌心穿出。对于负电荷，力的方向相反。该力始终垂直于 v 和 B，因此不做功——只改变速度的方向，不改变大小。
9. Circular Motion of a Charged Particle in a Uniform Magnetic Field | 匀强磁场中带电粒子的圆周运动
When a charged particle moves perpendicular to a uniform magnetic field, the magnetic force provides the centripetal force required for circular motion:
q v B = m v² / r
h: r = (m v) / (q B). The period T and frequency f of the motion are independent of speed:
T = 2π m / (q B) , f = q B / (2π m)
This principle is used in mass spectrometers and cyclotrons. If the velocity has a component parallel to the field, the particle moves in a helical path—combining circular motion with constant drift along the field lines.
当带电粒子垂直于匀强磁场运动时，磁力提供圆周运动所需的向心力：q v B = m v² / r。由此可导出圆轨道半径 r = (m v) / (q B)。运动的周期 T 和频率 f 与速率无关：T = 2π m / (q B)，f = q B / (2π m)。这一原理被用于质谱仪和回旋加速器。如果速度有平行于磁场的分量，粒子将做螺旋运动——在绕磁场线旋转的同时沿场线方向匀速漂移。
10. Force on a Current‑Carrying Conductor in a Magnetic Field | 载流导体在磁场中的受力
A straight conductor of length L carrying a current I in a magnetic field B experiences a force:
F = B I L sin θ
where θ is the angle between the direction of the current and the magnetic field. The direction is given by Fleming's left‑hand rule: with the first finger in the direction of B, the second finger in the direction of the conventional current I, the thumb points in the direction of the force (for a positive charge flow). This effect is the basis of electric motors and moving‑coil loudspeakers.
一段长为 L、通以电流 I 的直导体在磁场 B 中所受的力为 F = B I L sin θ，其中 θ 是电流方向与磁场方向的夹角。方向由弗莱明左手定则判定：将食指指向 B 的方向，中指指向电流 I 的方向，拇指所指即为导体受力方向。该效应是电动机和动圈式扬声器的工作原理。
11. Forces Between Parallel Current‑Carrying Wires | 平行电流之间的作用力
Two parallel wires carrying currents I₁ and I₂ separated by a distance d exert a magnetic force on each other. The force per unit length is:
F / L = μ₀ I₁ I₂ / (2π d)
gth placed 1 metre apart in vacuum, would produce a force of 2×10⁻⁷ newtons per metre of length.
两根平行导线，间距为 d，分别载有电流 I₁ 和 I₂，它们之间相互作用的磁力，单位长度上的受力为 F / L = μ₀ I₁ I₂ / (2π d)。电流同向时相吸，反向时相斥。这一关系是安培定义的基础：1 安培是指真空中相距 1 米的两根无限长平行直导线中通以等量恒定电流时，若每米长度上产生的力为 2×10⁻⁷ 牛顿，则导线中的电流为 1 安培。
12. The Hall Effect | 霍尔效应
When a current‑carrying conductor is placed in a perpendicular magnetic field, a voltage is produced across the conductor in a direction perpendicular to both the current and the magnetic field. This is the Hall effect. For a flat conductor of thickness t with charge carriers of charge q and drift velocity vᵈ, the Hall voltage VH is:
VH = B I / (n q t)
where n is the number density of charge carriers. The sign of the Hall voltage reveals whether the charge carriers are positive or negative. The Hall effect is used in probes to measure magnetic field strength and in sensors to determine the nature of charge carriers in semiconductors.
将载流导体置于垂直于电流方向的磁场中，则在导体两侧会产生一个既垂直于电流又垂直于磁场的电压，这就是霍尔效应。对于厚度为 t 的平板导体，若载流子电荷为 q、漂移速度为 vᵈ，则霍尔电压 VH = B I / (n q t)，其中 n 是载流子的数密度。霍尔电压的正负号揭示了载流子是正电荷还是负电荷。霍尔效应被用于测量磁场强度的探头以及判断半导体载流子类型的传感器。
Published by TutorHao | IB Physics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图