A-Level Physics: Force on a Current-Carrying Conductor Perpendicular to a Magnetic Field | A-Level 物理：电流垂直穿过磁场时的受力

📚 A-Level Physics: Force on a Current-Carrying Conductor Perpendicular to a Magnetic Field | A-Level 物理：电流垂直穿过磁场时的受力

In A-Level Physics (CIE), the behaviour of a current-carrying conductor in a magnetic field is a fundamental topic. When a straight wire carrying an electric current is placed perpendicular to a uniform magnetic field, it experiences a force that is perpendicular to both the current direction and the magnetic field direction. This force is the basis of electric motors, loudspeakers, and many measuring instruments.

在 CIE 的 A-Level 物理中，载流导线在磁场中的行为是一个基础课题。当一根通有电流的直导线垂直于匀强磁场放置时，它会受到一个既垂直于电流方向又垂直于磁场方向的力。这个力是电动机、扬声器以及许多测量仪器的基础。

1. Introduction to Magnetic Force on a Current-Carrying Wire | 载流导线在磁场中受力简介

A magnetic field exerts a force on a moving charge. Since an electric current is a flow of charges, a current-carrying wire placed in a magnetic field experiences a force. This is due to the Lorentz force acting on the individual moving electrons within the wire.

磁场对运动电荷施加力。由于电流是电荷的定向移动，置于磁场中的载流导线就会受力。这是磁场对导线内各个运动电子的洛伦兹力作用的结果。

When the current is perpendicular to the magnetic field, the magnitude of this force is given by the simple product of the magnetic flux density B, the current I, and the length of the wire L within the field.

当电流垂直于磁场时，该力的大小可以简单地表示为磁通密度 B、电流 I 和处于磁场中的导线长度 L 的乘积。

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2. The Equation F = BIL and Its Conditions | 公式 F = BIL 及其适用条件

The magnetic force on a straight wire is calculated using:

直导线所受的磁力计算公式为：

F = B I L

where F is the force in newtons (N), B is the magnetic flux density in tesla (T), I is the current in amperes (A), and L is the length of the conductor in the magnetic field in metres (m).

其中 F 是力，单位牛顿 (N)；B 是磁通密度，单位特斯拉 (T)；I 是电流，单位安培 (A)；L 是导体在磁场中的长度，单位米 (m)。

This equation is valid only when the conductor is perpendicular to the magnetic field. If the angle θ between the wire and the field is 90°, the full component of B is used. If the wire is parallel to the field, the force is zero.

该公式仅在导体垂直于磁场时成立。当导线与磁场的夹角 θ 为 90° 时，使用 B 的全部分量。若导线平行于磁场，则力为零。

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3. Why is the Force Maximum When Perpendicular? | 为什么垂直时受力最大？

The general expression for the force on a current-carrying wire in a magnetic field is F = B I L sin θ, where θ is the angle between the wire and the magnetic field direction. Since sin 90° = 1, placing the wire perpendicular gives the maximum possible force for a given B, I, and L.

载流导线在磁场中受力的通用表达式为 F = B I L sin θ，其中 θ 是导线与磁场方向之间的夹角。由于 sin 90° = 1，在给定的 B、I 和 L 下，导线垂直放置时得到最大可能的力。

This relationship highlights that only the component of the magnetic field perpendicular to the current contributes to the force. In vector terms, the force is given by the cross product F = I L × B, so its magnitude equals B I L sin θ.

这个关系式表明，只有垂直于电流方向的磁场分量才对力有贡献。用矢量表示，力等于叉积 F = I L × B，其大小为 B I L sin θ。

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4. Fleming’s Left-Hand Rule | 弗莱明左手定则

To determine the direction of the force, we use Fleming’s left-hand rule. Hold your left hand so that the thumb, first finger, and second finger are mutually perpendicular:

为了确定力的方向，我们使用弗莱明左手定则。将左手拇指、食指和中指相互垂直：

• First finger points in the direction of the magnetic field (from N to S).

  食指指向磁场方向（从 N 极到 S 极）。

• Second finger points in the direction of the current (conventional current from + to -).

  中指指向电流方向（正电荷流动方向，即从 + 到 -）。

• Thumb then points in the direction of the force experienced by the conductor.

  拇指则指向导体所受力的方向。

Note that this rule applies to conventional current direction, not electron flow. If you use electron flow, the force direction would be opposite.

注意此定则适用于传统电流方向，而非电子流动方向。如果使用电子流方向，力的方向会相反。

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5. Force on a Wire at an Angle | 导线与磁场成角度时的受力

When the wire is not perpendicular to the magnetic field, the force is reduced by the sine of the angle:

当导线不垂直于磁场时，力会乘以夹角的正弦值：

F = B I L sin θ

For θ = 90°, F = BIL; for θ = 0° (parallel), F = 0. This equation is essential for solving problems where the wire is tilted relative to the field.

当 θ = 90° 时，F = BIL；当 θ = 0°（平行）时，F = 0。这个公式对于求解导线相对磁场倾斜的问题至关重要。

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6. Worked Example: Calculating the Force | 例题：计算安培力

Example: A 0.50 m length of wire carries a current of 3.0 A and lies perpendicular to a uniform magnetic field of magnetic flux density 0.20 T. Calculate the force on the wire.

例题：一根长度为 0.50 m 的导线通有 3.0 A 的电流，垂直于磁通密度为 0.20 T 的匀强磁场放置。求导线所受的力。

F = B I L = 0.20 T × 3.0 A × 0.50 m = 0.30 N

Thus, the force on the wire is 0.30 N. The direction would be determined using Fleming’s left-hand rule.

因此，导线所受的力为 0.30 N。方向可用弗莱明左手定则来确定。

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7. Common Mistakes and Exam Tips | 常见错误与考试技巧

• Forgetting that F = BIL only applies when the wire is perpendicular to the magnetic field. Always check the angle.

  忘记 F = BIL 仅在导线垂直于磁场时适用。务必检查角度。

• Using the length of the whole wire instead of only the length inside the magnetic field.

  使用整根导线的长度而非处于磁场内的那部分长度。

• Confusing Fleming’s left-hand rule (for force) with Fleming’s right-hand rule (for induced current).

  混淆弗莱明左手定则（用于受力）和弗莱明右手定则（用于感应电流）。

• When expressing the unit tesla, remember 1 T = 1 N A⁻¹ m⁻¹.

  表示特斯拉单位时，记住 1 T = 1 N A⁻¹ m⁻¹。

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8. Applications in Everyday Life | 日常生活中的应用

The force on a current-carrying wire in a magnetic field is exploited in many devices. In an electric motor, a coil of wire experiences a torque when current flows through it while placed in a magnetic field, causing rotation.

载流导线在磁场中受力的原理被应用于许多设备中。在电动机中，通电线圈在磁场中受到力矩作用，从而产生转动。

Loudspeakers and headphones also rely on this force: an audio signal current flows through a coil placed in a magnetic field, causing the coil and attached diaphragm to vibrate and produce sound.

扬声器和耳机也依赖这个力：音频信号电流通过置于磁场中的线圈，使线圈及其连接的振膜振动并发出声音。

Electrical measuring instruments such as the moving-coil galvanometer also use this principle to deflect a pointer in proportion to the current.

动圈式电流计等电测仪器也利用这一原理，使指针偏转角度与电流成正比。

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9. Connecting to the Lorentz Force | 与洛伦兹力的联系

At the microscopic level, the force on the wire arises from the magnetic force on individual moving charges, each of magnitude F = q v B sin θ, where q is the charge, v is its drift velocity, and θ is the angle between v and B.

在微观层面，导线所受的力源于各个运动电荷所受的磁力，每个电荷受力的大小为 F = q v B sin θ，其中 q 是电荷量，v 是漂移速度，θ 是 v 与 B 之间的夹角。

The macroscopic expression F = B I L is derived by summing the forces on all the charge carriers in the wire. This connection helps students understand both phenomena from a unified perspective.

宏观表达式 F = B I L 是通过对导线内所有载流子所受的力求和推导得出的。这种联系有助于学生从统一的角度理解这两种现象。

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10. Summary | 总结

When a current-carrying conductor is placed perpendicular to a magnetic field, it experiences a force F = B I L, with the direction given by Fleming’s left-hand rule. For a general angle, F = B I L sin θ. This principle is central to electromagnetism and has numerous practical applications.

当载流导体垂直于磁场放置时，它受到的力为 F = B I L，方向由弗莱明左手定则决定。对于一般角度，F = B I L sin θ。这一原理是电磁学的核心，并且有众多实际应用。

Understanding the distinction between the perpendicular and angled cases is essential for solving A-Level questions successfully.

理解垂直与倾斜两种情况之间的区别对于成功解答 A-Level 考题至关重要。

Published by TutorHao | Physics Revision Series | aleveler.com

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