📚 Magnetism Due to Electric Current and Applications | IB物理：电流的磁效应与应用
In IB Physics, the magnetic effect of an electric current is a fundamental topic that connects electricity and magnetism. This article covers the key concepts, mathematical relationships, and real-world applications required for the IB syllabus.
在IB物理中，电流的磁效应是连接电与磁的核心主题。本文围绕IB考纲，系统讲解基本概念、定量关系及实际应用，帮助同学们精准掌握考点。
1. Oersted's Experiment | 奥斯特实验
In 1820, Hans Christian Oersted discovered that a compass needle deflects when placed near a current-carrying wire. This was the first evidence that electric currents produce magnetic fields.
1820年，奥斯特发现，将指南针放在通电导线附近时，磁针会发生偏转。这一发现首次证明了电流能够产生磁场。
- When the current flows from south to north, the north pole of the compass deflects to the east.
- When the current direction is reversed, the compass deflects in the opposite direction.
- The deflection disappears when the current is switched off, proving that the magnetic field is caused by the current.
- 当电流由南向北流动时，指南针北极向东偏转。
- 当电流反向时，指南针的偏转方向也随之反向。
- 断开电流后偏转消失，说明磁场是由电流产生的。
The magnetic field lines form concentric circles around a straight current-carrying wire.
通电直导线周围的磁感线是以导线为圆心的同心圆。
2. Right-Hand Grip Rule | 右手螺旋定则（安培定则）
To determine the direction of the magnetic field around a current-carrying wire, use the right-hand grip rule: grasp the wire with the right hand with the thumb pointing in the direction of conventional current; the curled fingers point in the direction of the magnetic field.
判断通电直导线周围磁场方向使用右手螺旋定则：用右手握住导线，拇指指向电流方向，弯曲的四指所指方向即为磁场方向。
- For a straight wire: the field is circular around the wire.
- For a solenoid: the fingers curl in the direction of current, and the thumb points to the north pole of the solenoid.
- 对直导线：磁场呈同心圆状环绕导线。
- 对螺线管：四指弯曲方向为电流方向，拇指指向螺线管的N极。
B = μ₀I / (2πr) (for a long straight wire, where μ₀ = 4π × 10⁻⁷ T·m·A⁻¹)
B = μ₀I / (2πr)（无限长直导线，其中 μ₀ = 4π × 10⁻⁷ T·m·A⁻¹）
3. Magnetic Field of a Solenoid | 螺线管的磁场
A solenoid is a coil of wire wound in a helix. When a current passes through it, the magnetic field inside is nearly uniform and strong.
螺线管是将导线绕成螺旋形的线圈。通电后，其内部磁场近似均匀且较强。
- Inside a long solenoid, the magnetic field is approximately parallel to the axis.
- The field strength depends on the current, the number of turns per unit length, and the core material.
- 长螺线管内部磁场近似平行于轴线。
- 磁场强弱与电流、单位长度匝数及铁芯材料有关。
B = μ₀nI (n = number of turns per unit length)
B = μ₀nI（n为单位长度匝数）
The right-hand grip rule for a solenoid: wrap your right hand around the coil so that your fingers point in the direction of the current; your thumb points toward the north pole.
螺线管的右手螺旋定则：右手四指沿电流方向弯曲，拇指所指方向即为N极。
4. Magnetic Force on a Current-Carrying Conductor | 通电导线在磁场中的安培力
A current-carrying conductor placed in an external magnetic field experiences a force. This is known as the Ampere force.
通电导线置于外磁场中会受到力的作用，这种力称为安培力。
F = BIL sin θ
Where F is the force (N), B is the magnetic flux density (T), I is the current (A), L is the length of the conductor inside the field (m), and θ is the angle between the wire and the magnetic field direction.
其中 F 为安培力（N），B 为磁感应强度（T），I 为电流（A），L 为处于磁场中的导线长度（m），θ 为导线与磁场方向之间的夹角。
- When the wire is perpendicular to the field, θ = 90°, F = BIL.
- When the wire is parallel to the field, θ = 0°, F = 0.
- 当导线与磁场垂直时，θ = 90°，F = BIL。
- 当导线与磁场平行时，θ = 0°，F = 0。
5. Fleming's Left-Hand Rule | 弗莱明左手定则
To determine the direction of the force on a current-carrying conductor in a magnetic field, use Fleming's left-hand rule: thumb represents Force, index finger represents Field (B), and middle finger represents Current (I).
判断安培力方向使用弗莱明左手定则：拇指指向力F方向，食指指向磁场B方向，中指指向电流I方向。
- Ensure that the three fingers are mutually perpendicular.
- The rule applies to both straight wires and individual charge carriers.
- 注意三个手指相互垂直。
- 该定则适用于直导线及单个运动电荷。
6. Magnetic Flux Density and Magnetic Flux | 磁感应强度与磁通量
Magnetic flux density B is a vector quantity that describes the strength and direction of a magnetic field. It is defined by the force on a current-carrying conductor.
磁感应强度 B 是描述磁场强弱和方向的矢量，可由通电导线所受安培力来定义。
B = F / (IL) (when wire is perpendicular to field)
B = F / (IL)（导线垂直于磁场时）
Magnetic flux Φ through an area A is given by:
磁通量 Φ 通过面积 A 的定义为：
Φ = BA cos θ
agnetic field direction. The unit of magnetic flux is the weber (Wb), where 1 Wb = 1 T·m².
其中 θ 为面积法线与磁场方向的夹角。磁通量单位为韦伯（Wb），1 Wb = 1 T·m²。
7. Force on a Moving Charge | 运动电荷在磁场中的力（洛伦兹力）
When a charged particle moves through a magnetic field, it experiences a force called the Lorentz force. This is the microscopic origin of the Ampere force.
带电粒子在磁场中运动时受到的力称为洛伦兹力，这是安培力的微观本质。
F = qvB sin θ
where q is the charge, v is the speed of the particle, and θ is the angle between v and B.
其中 q 为电荷量，v 为粒子速度，θ 为 v 与 B 之间的夹角。
- v is perpendicular to B, the particle moves in a circular path with radius r = mv / (qB).
- The Lorentz force does no work because it always acts perpendicular to the velocity.
- 若 v 垂直于 B，粒子做匀速圆周运动，轨道半径 r = mv / (qB)。
- 洛伦兹力始终垂直于速度，因此不做功。
8. The Ampere – Definition | 安培的定义
In the SI system, the ampere is defined using the magnetic force between two parallel current-carrying wires.
在国际单位制中，安培是利用两根平行通电导线之间的磁力来定义的。
rrent of 1 ampere, produce a force of exactly 2 × 10⁻⁷ N per metre of length between them.
两根无限长且平行的细直导线，在真空中相距1米，通以1安培的稳定电流时，每米长度上产生的相互作用力恰好为 2 × 10⁻⁷ 牛。
F / L = μ₀I₁I₂ / (2πd)
F / L = μ₀I₁I₂ / (2πd)
9. Applications: Electric Motor | 应用：电动机
An electric motor converts electrical energy into mechanical energy using the magnetic force on a current-carrying coil.
电动机利用通电线圈在磁场中受安培力作用，将电能转化为机械能。
- A rectangular coil is placed in a uniform magnetic field and carries a current.
- Opposite sides of the coil experience forces in opposite directions, producing a torque.
- A commutator reverses the current every half turn so the coil continues rotating in the same direction.
- 矩形线圈置于匀强磁场中并通有电流。
- 线圈两侧受到方向相反的力，形成力矩。
- 换向器每半圈改变一次电流方向，使线圈持续沿同一方向转动。
Torque τ = B I A N cos θ (where A is the area of the coil and N is the number of turns)
力矩 τ = B I A N cos θ（A为线圈面积，N为匝数）
10. Applications: Electromagnet | 应用：电磁铁
An electromagnet consists of a solenoid wrapped around a soft iron core. Its magnetic field can be switched on and off by controlling the current.
电磁铁由绕在软铁芯上的螺线管构成，通过控制电流可以控制磁场的有无。
- Soft iron is used because it magnetises easily and loses its magnetism quickly when the current stops.
- Stronger currents and more turns per unit length produce a stronger magnetic field.
- Electromagnets are used in cranes, electric bells, relay switches, and MRI machines.
- 选用软铁是因为它易磁化，且断电后磁性迅速消失。
- 增大电流或增加单位长度匝数可以增强磁场。
- 电磁铁广泛应用于起重机、电铃、继电器开关和核磁共振成像设备等。
11. Applications: Moving Coil Galvanometer | 应用：电流计
A moving coil galvanometer is a sensitive device used to detect and measure small electric currents. It works on the principle that a current-carrying coil placed in a magnetic field experiences a torque.
电流计是一种用于检测和测量微小电流的灵敏仪器，其原理是通电线圈在磁场中受到力矩作用。
- A coil is mounted on a pivot in a radial magnetic field.
- A spring provides a restoring torque proportional to the angle of deflection.
- The deflection is proportional to the current, allowing a calibrated scale to read the current.
- 线圈安装在枢轴上，置于辐射状磁场中。
- 游丝提供与偏转角成正比的恢复力矩。
- 偏转角度与电流成正比，通过标定刻度即可读取电流值。
12. Key Ideas for IB Exams | IB考试要点总结
Here are the most important points to remember for your IB Physics exam on this topic.
以下是IB物理考试中本主题最重要的考点总结。
| Concept | Formula / Rule |
| Oersted effect | Current produces magnetic field |
| Straight wire field | B = μ₀I / (2πr) |
| Solenoid field | B = μ₀nI |
| Ampere force | F = BIL sin θ |
| Direction of force | Fleming's left-hand rule |
| Magnetic flux | Φ = BA cos θ |
| Lorentz force | F = qvB sin θ |
| 概念 | 公式 / 规则 |
| 奥斯特效应 | 电流产生磁场 |
| 直导线磁场 | B = μ₀I / (2πr) |
| 螺线管磁场 | B = μ₀nI |
| 安培力 | F = BIL sin θ |
| 力的方向 | 弗莱明左手定则 |
| 磁通量 | Φ = BA cos θ |
| 洛伦兹力 | F = qvB sin θ |
Always remember to use the right-hand grip rule for the field direction, Fleming' rule for the force direction, and check the angle θ carefully when applying F = BIL sin θ.
请务必牢记：用右手螺旋定则判断磁场方向，用弗莱明左手定则判断安培力方向，并仔细检查 F = BIL sin θ 中的夹角 θ。
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