A-Level Physics: Definition and Units of Magnetic Flux Density | A-Level 物理：磁通量密度的定义与单位

📚 A-Level Physics: Definition and Units of Magnetic Flux Density | A-Level 物理：磁通量密度的定义与单位

Magnetic flux density is one of the most important concepts in A-Level physics, especially in the CIE syllabus. It connects magnetic forces, electric currents, and the geometry of magnetic fields into a single measurable quantity. This article explains its definition, the equation used to define it, its units, and common exam applications.

磁通量密度是 A-Level 物理（尤其是 CIE 考纲）中最核心的概念之一。它将磁力、电流和磁场的几何形状联系成一个可测量的物理量。这篇文章将讲解它的定义、定义式、单位以及常见考点应用。

1. What Is Magnetic Flux Density? | 什么是磁通量密度？

Magnetic flux density, usually given the symbol B, describes how strong and how concentrated a magnetic field is at a particular point. It is a vector quantity, meaning it has both magnitude and direction. The direction of B is the direction in which a tiny north pole would experience a force, or equivalently, the direction of the field lines.

磁通量密度通常用符号 B 表示，用来描述磁场在某一点的强弱与密集程度。它是一个矢量，既有大小也有方向。B 的方向是小磁针北极受力方向，也就是磁场线的切线方向。

Although many students first meet B in the context of the force on a current-carrying wire, the formal definition relies on that very force. The SI unit of B is the tesla (T), named after Nikola Tesla.

虽然很多同学首次接触 B 是在电流导线受力的场景中，但 B 的正式定义恰恰依赖这个力。B 的国际单位是特斯拉（T），以尼古拉·特斯拉命名。

2. The Defining Equation: F = BIL sin θ | 定义式：F = BIL sin θ

For a straight wire of effective length L carrying a current I inside a uniform magnetic field of flux density B, the magnetic force F on the wire is given by:

对于一段有效长度为 L、通有电流 I 的直导线，处于磁通量密度为 B 的匀强磁场中时，导线受到的磁力 F 为：

F = B I L sin θ

Here, θ is the angle between the direction of the current and the direction of the magnetic field. When the wire is perpendicular to the field, θ = 90° and sin θ = 1, so the force is maximum:

其中 θ 是电流方向与磁场方向之间的夹角。当导线垂直于磁场时，θ = 90°，sin θ = 1，力达到最大值：

F = B I L

This maximum-force case is used to define B. Rearranging gives:

这个最大力的情况被用来定义 B。整理后得到：

B = F / (I L)

Thus magnetic flux density can be defined as the force per unit current per unit length acting on a straight conductor placed perpendicular to the magnetic field.

因此磁通量密度可以定义为：垂直于磁场的直导线，单位电流、单位长度上所受到的磁力。

3. Alternative Definition: Magnetic Flux per Unit Area | 另一种定义：单位面积上的磁通量

Magnetic flux density is also related to magnetic flux Φ. Magnetic flux is the total number of magnetic field lines passing through a given area, while flux density is the concentration of those lines per unit area. For a uniform field perpendicular to a plane of area A:

磁通量密度还与磁通量 Φ 有关。磁通量是穿过某一面积的总磁场线数，而磁通量密度是单位面积上磁场线的密集程度。对于匀强磁场且方向垂直于面积为 A 的平面时：

Φ = B A

If the field is not perpendicular to the area, a cos θ factor is needed, where θ is the angle between the magnetic field direction and the normal to the area:

如果磁场不垂直于平面，则需要乘以 cos θ，其中 θ 是磁场方向与平面法线之间的夹角：

Φ = B A cos θ

Because the tesla can be expressed as a weber per square metre (Wb m⁻²), B can be thought of as “flux per unit area.” This is why it is called flux density.

因为特斯拉也可以表示为韦伯每平方米（Wb m⁻²），所以 B 可以被理解为“单位面积上的磁通量”。这就是为什么它被称为磁通量密度。

4. Unit of Magnetic Flux Density: The Tesla | 磁通量密度的单位：特斯拉

From B = F / (I L), we can derive the tesla in base SI units. Force F has units of newtons (N = kg m s⁻²), current I has units of amperes (A), and length L has units of metres (m). Therefore:

从 B = F / (I L) 出发，我们可以推导出特斯拉用 SI 基本单位表示的形式。力 F 的单位是牛顿（N = kg m s⁻²），电流 I 的单位是安培（A），长度 L 的单位是米（m）。因此：

1 T = 1 N A⁻¹ m⁻¹ = 1 kg A⁻¹ s⁻²

Equivalently, using the flux definition Φ = B A, we have:

等效地，从磁通量定义 Φ = B A 可得：

1 T = 1 Wb m⁻²

So one tesla is the flux density that produces a force of 1 newton on a 1 metre wire carrying a current of 1 ampere, when the wire is perpendicular to the field.

因此，1 特斯拉是：当 1 米长导线通有 1 安培电流且垂直磁场放置时，受到 1 牛顿磁力所对应的磁通量密度。

5. Magnetic Flux Density and Moving Charges | 磁通量密度与运动电荷

A charged particle moving with velocity v through a magnetic field B experiences a magnetic force. For a charge q, the magnitude of the force is:

带电粒子以速度 v 在磁场 B 中运动时，会受到磁力。对于电荷 q，力的大小为：

F = q v B sin θ

where θ is the angle between the velocity and the magnetic field direction. When the charge moves perpendicular to the field, sin θ = 1 and F = qvB. This equation is often used in circular motion problems involving charged particles in magnetic fields.

其中 θ 是速度方向与磁场方向的夹角。当电荷垂直磁场运动时，sin θ = 1，F = qvB。这个公式常用于解带电粒子在磁场中做圆周运动的题目。

This relationship is also a possible way to define B: the magnetic flux density is the force acting on a unit charge moving at unit velocity perpendicular to the field.

这一关系也可以用来定义 B：磁通量密度是单位电荷以单位速度垂直磁场运动时所受到的磁力。

6. Magnetic Flux Density vs Magnetic Flux | 磁通量密度与磁通量的区别

Students often confuse magnetic flux density B and magnetic flux Φ. The table below summarises the key differences.

同学们经常混淆磁通量密度 B 和磁通量 Φ。下表总结了它们的核心区别。

Quantity	Magnetic Flux Density B	Magnetic Flux Φ
Nature	Vector (strength of field at a point)	Scalar (total field lines through an area)
Symbol	B	Φ
SI unit	tesla (T)	weber (Wb)
Related formula	B = F / (IL)	Φ = B A cos θ

Note that Φ depends on the area through which the field passes, while B is a local property of the field. A strong field can have a small flux if the area is tiny; a weak field can have a large flux if the area is huge.

注意：Φ 取决于磁场穿过的面积，而 B 是磁场的局部属性。场很强但面积很小时，磁通量可能很小；场很弱但面积很大时，磁通量也可能很大。

7. Worked Example: Calculating Force from B | 例题：由 B 计算磁力

A straight wire of length 0.20 m carries a current of 4.0 A and is placed in a uniform magnetic field of flux density 0.30 T. The wire is perpendicular to the field. Calculate the magnetic force on the wire.

一根长为 0.20 m 的直导线通有 4.0 A 的电流，放在磁通量密度为 0.30 T 的匀强磁场中，导线与磁场垂直。求导线所受磁力。

Since the wire is perpendicular to the field, sin θ = 1. Using F = BIL:

因为导线垂直于磁场，sin θ = 1。利用 F = BIL：

F = 0.30 × 4.0 × 0.20 = 0.24 N

The force is 0.24 N. Use Fleming’s left-hand rule to determine the direction if required.

力为 0.24 N。如果需要确定方向，可以用弗莱明左手定则。

If the wire were at 30° to the field instead, then θ = 30° and:

如果导线与磁场夹角为 30°，则 θ = 30°，于是：

F = 0.30 × 4.0 × 0.20 × sin 30° = 0.12 N

This smaller value shows why the sin θ factor is essential in the general formula.

这个较小的值说明为什么通用公式中的 sin θ 因子必不可少。

8. Worked Example: Determining B from Measurements | 例题：由测量值求 B

A student places a 5.0 cm wire at right angles to a magnetic field. When a current of 2.0 A flows, the wire experiences a force of 0.015 N. What is the magnetic flux density?

学生将一根 5.0 cm 的导线垂直放入磁场中，当通过 2.0 A 电流时，导线受到 0.015 N 的力。求磁通量密度。

First convert length to metres: L = 0.050 m. Since the wire is perpendicular to the field, rearrange B = F / (IL):

首先将长度换算为米：L = 0.050 m。由于导线垂直磁场，整理 B = F / (IL)：

B = 0.015 / (2.0 × 0.050) = 0.15 T

So the flux density is 0.15 T.

因此磁通量密度为 0.15 T。

9. Common Exam Misconceptions | 常见考试误区

Using the wrong angle: The angle θ in F = BIL sin θ is the angle between the current direction and the magnetic field direction, not the angle with the normal to the plane.

角度用错：F = BIL sin θ 中的 θ 是电流方向与磁场方向的夹角，而不是与平面法线的夹角。
Forgetting the sin θ factor: When the wire is parallel to the field, θ = 0° and the force is zero. Some students still use F = BIL.

忘记 sin θ 因子：当导线平行于磁场时，θ = 0°，力为零。有些同学仍然使用 F = BIL。
Confusing B and Φ: B has units T, Φ has units Wb. In exam questions, check whether the area is already included.

混淆 B 与 Φ：B 的单位是 T，Φ 的单位是 Wb。做题目时注意面积是否已经包含在内。
Not converting units: Length must be in metres, area in square metres, and force in newtons before substituting into formulas.

未换算单位：代入公式前，长度必须用米，面积必须用平方米，力必须用牛顿。

10. Key Points for Revision | 复习要点

Magnetic flux density B is a vector quantity representing the strength of a magnetic field at a point.

磁通量密度 B 是矢量，代表磁场在某一点的强弱。
The defining equation is B = F / (IL) for a wire perpendicular to the field.

定义式为 B = F / (IL)，适用于导线垂直磁场的情况。
The SI unit is the tesla: 1 T = 1 N A⁻¹ m⁻¹ = 1 Wb m⁻² = 1 kg A⁻¹ s⁻².

国际单位是特斯拉：1 T = 1 N A⁻¹ m⁻¹ = 1 Wb m⁻² = 1 kg A⁻¹ s⁻²。
The general force equation is F = BIL sin θ; the force is maximum when the wire is perpendicular to B and zero when parallel.

通用力公式是 F = BIL sin θ；导线垂直于 B 时力最大，平行于 B 时力为零。
Magnetic flux density can also be related to flux by Φ = B A cos θ; therefore B = Φ / (A cos θ).

磁通量密度也可通过 Φ = B A cos θ 与磁通量联系；因此 B = Φ / (A cos θ)。

With these definitions and formulas, you can confidently solve CIE A-Level problems on magnetic flux density and connect them to forces on currents and moving charges.

掌握了这些定义和公式，你就能自信地解决 CIE A-Level 中关于磁通量密度的问题，并将其与电流受力和运动电荷受力联系起来。

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A-Level Physics: Definition and Units of Magnetic Flux Density | A-Level 物理：磁通量密度的定义与单位