Magnetism Due to Electric Current and Applications | IB物理：电流的磁效应与应用

📚 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

where θ is the angle between the normal to the area and the magnetic 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。

If 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。

Two thin, straight, parallel conductors of infinite length, placed 1 metre apart in a vacuum, each carrying a current 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)

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’s left-hand 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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Magnetism Due to Electric Current and Applications | IB物理：电流的磁效应与应用