Producing and representing magnetic fields | 磁场的产生与表示

📚 Producing and representing magnetic fields | 磁场的产生与表示

Magnetic fields are produced by moving charges and by permanent magnets. Representing these fields accurately through field lines is a core skill in A-Level Physics, especially for CIE exam questions on electromagnetism.

磁场由运动电荷和永磁体产生。用磁力线准确表示这些场是 A-Level 物理的核心技能，尤其是在 CIE 电磁学考题中。

1. Magnetic fields and field lines | 磁场与磁力线

A magnetic field is a region of space in which a magnetic pole, a moving charge or a current-carrying conductor experiences a force. The direction of the field at any point is defined as the direction of the force experienced by a small north pole placed at that point.

磁场是空间中的一个区域，在该区域内磁极、运动电荷或载流导体会受到力的作用。任一点的磁场方向定义为放在该点的小磁针 N 极所受力的方向。

Field lines, also called magnetic flux lines, show the direction and relative strength of a magnetic field. They are drawn as arrows pointing from north to south outside a magnet.

磁力线又称磁通线，用于表示磁场的方向和相对强弱。磁力线用带箭头的线画出，在磁铁外部从 N 极指向 S 极。

2. Representing fields with compasses and iron filings | 用指南针和铁屑表示磁场

A plotting compass is a small magnetised needle that is free to rotate. When placed in a magnetic field, the needle aligns with the field direction at that point. By moving the compass step by step, the shape of the field can be mapped accurately.

一个袖珍罗盘是一根可自由转动的小磁针。当它放入磁场时，磁针会沿该点的磁场方向排列。逐步移动罗盘，就可以准确地描绘出磁场的形状。

Iron filings can also reveal field patterns. Each filing becomes a tiny induced magnet and lines up along the field lines, producing a visible pattern around a magnet or a current-carrying conductor.

铁屑也能显示磁场分布。每粒铁屑会被磁化成微小的感应磁体，并沿磁力线排列，从而在磁体或载流导体周围形成可见的图案。

3. Field line conventions | 磁力线绘制规则

Magnetic field lines are continuous closed loops. Outside a magnet, they run from the north pole to the south pole. Inside the magnet, they continue from the south pole back to the north pole.

磁力线是连续的闭合曲线。在磁铁外部，它们从 N 极出发指向 S 极。在磁铁内部，它们从 S 极继续回到 N 极。

The spacing of field lines indicates field strength: closely spaced lines represent a strong field, while widely spaced lines represent a weak field. Field lines never cross each other because the magnetic field has a unique direction at every point.

磁力线的疏密表示磁场强弱：线越密表示磁场越强，线越疏表示磁场越弱。磁力线永不相交，因为磁场在每一点都有唯一的方向。

4. Magnetic fields from permanent magnets | 永磁体的磁场

A bar magnet produces a characteristic field pattern. Near the poles the field is strongest, and the field lines spread out and curve around from the north pole to the south pole.

条形磁铁产生特有的磁场分布。两极附近磁场最强，磁力线从 N 极发出并向周围散开，弯曲回到 S 极。

Two unlike poles attract because their field lines connect from north to south between the magnets. Two like poles repel because the opposing field lines push against one another.

异名磁极相互吸引，因为磁力线在两磁铁之间从 N 极连接到 S 极。同名磁极相互排斥，因为方向相反的磁力线互相推挤。

5. Current-carrying straight conductor | 载流直导线的磁场

An electric current in a straight wire produces a magnetic field around the wire. The field lines form concentric circles centred on the wire, lying in planes perpendicular to the wire.

直导线中的电流会在导线周围产生磁场。磁力线是以导线为中心的同心圆，位于与导线垂直的平面内。

The direction of the circular field is determined by the direction of the conventional current. The field strength decreases with distance from the wire, so the circles are drawn further apart as the radius increases.

环形磁场的方向由传统电流方向决定。磁场强度随离导线的距离增大而减弱，因此随着半径增大，同心圆画得越来越疏。

For a long straight wire, the magnetic flux density at a perpendicular distance r from the wire carrying current I is given by:

对于长直导线，在与载流 I 的导线垂直距离 r 处，磁通量密度为：

B = μ₀ I / (2π r)

where μ₀ is the permeability of free space.

其中 μ₀ 为真空磁导率。

6. Right-hand grip rule for a straight wire | 直导线右手螺旋定则

To find the field direction around a straight conductor, point the thumb of the right hand in the direction of the conventional current. The curled fingers then show the direction of the circular magnetic field lines.

要判断直导线周围的磁场方向，将右手拇指指向传统电流方向。弯曲的四指就表示环形磁力线的方向。

This is called the right-hand grip rule. If the current is reversed, the magnetic field direction also reverses at every point around the wire.

这称为右手螺旋定则。如果电流反向，导线周围每一点的磁场方向也跟着反向。

7. Magnetic field of a flat circular coil | 平面圆形线圈的磁场

A single loop of wire carrying a current produces a magnetic field similar to that of a short bar magnet. The field lines pass through the centre of the loop and curve around the outside.

载流的单匝线圈产生的磁场类似于短条形磁铁。磁力线穿过线圈中心，并在外部弯曲形成回路。

At the centre of a flat circular coil, the field is uniform over a small region and perpendicular to the plane of the coil. For N turns, the magnetic flux density at the centre is given by:

在平面圆形线圈中心，较小区域内磁场均匀且垂直于线圈平面。对于 N 匝线圈，中心的磁通量密度为：

B = μ₀ N I / (2 r)

where r is the radius of the coil and I is the current in each turn.

其中 r 为线圈半径，I 为每匝线圈中的电流。

8. Magnetic field of a long solenoid | 长直螺线管的磁场

A long solenoid is a coil of wire with many closely spaced turns. When current flows through it, the magnetic field inside the solenoid is strong and nearly uniform, while the field outside is weak.

长直螺线管是由许多紧密排列的线圈组成的螺线管。当电流通过时，螺线管内部的磁场强而几乎均匀，外部的磁场很弱。

The field pattern of a solenoid is very similar to that of a bar magnet, with one end acting as a north pole and the other as a south pole.

螺线管的磁场分布与条形磁铁非常相似，一端相当于 N 极，另一端相当于 S 极。

For an ideal long solenoid, the magnetic flux density inside is given by:

对于理想长螺线管，内部的磁通量密度为：

B = μ₀ n I

where n is the number of turns per unit length, equal to N / L for a solenoid with N turns and length L.

其中 n 是单位长度的匝数，对于匝数为 N、长度为 L 的螺线管，n = N / L。

9. Right-hand grip rule for a solenoid | 螺线管右手定则

To identify the poles of a current-carrying solenoid, grip the solenoid with the right hand so that the curled fingers follow the conventional current direction through the coils. The outstretched thumb then points towards the north pole of the solenoid.

要判断载流螺线管的磁极，用右手握住螺线管，使弯曲的四指沿线圈中传统电流方向。伸直的拇指就指向螺线管的 N 极。

Reversing the current direction reverses the polarity of the solenoid, so the north and south poles swap ends.

改变电流方向会反转螺线管的极性，使 N 极和 S 极互换位置。

10. Magnetic flux density B and units | 磁通量密度 B 与单位

Magnetic field strength is described quantitatively by the magnetic flux density B. It is defined by the force on a current-carrying conductor in a magnetic field:

磁场强度用磁通量密度 B 来定量描述。它由磁场中载流导体所受的力定义：

B = F / (I L sin θ)

where F is the force on a conductor of length L carrying current I at an angle θ to the field.

其中 F 是长度为 L、载流为 I 的导体与磁场方向成 θ 角时所受的力。

The SI unit of magnetic flux density is the tesla, symbol T. One tesla is equal to one newton per ampere per metre, written as:

磁通量密度的国际单位是特斯拉，符号为 T。1 特斯拉等于 1 牛顿每安培每米，写作：

1 T = 1 N A⁻¹ m⁻¹

Magnetic flux density can also be expressed as magnetic flux per unit area: B = Φ / A. Therefore 1 T = 1 Wb m⁻².

磁通量密度也可表示为单位面积的磁通量：B = Φ / A。因此 1 T = 1 Wb m⁻²。

11. Representing uniform fields | 均匀磁场的表示

A uniform magnetic field is represented by parallel, equally spaced field lines. This indicates that the field strength and direction are the same at every point in the region.

均匀磁场用平行且等间距的磁力线表示。这表示该区域内各点的磁场强度和方向都相同。

Uniform fields are produced between flat, opposite magnetic poles and inside long solenoids. The field lines between two opposite poles run straight from the north pole to the south pole.

均匀磁场可在两平行的异名磁极之间以及长螺线管内部产生。两异名磁极之间的磁力线从 N 极直接指向 S 极。

In diagrams, uniform fields are often shown by a set of parallel arrows with equal spacing, confirming constant magnetic flux density B.

在图中，均匀磁场通常用一组等距的平行箭头表示，以说明磁通量密度 B 恒定。

12. Earth’s magnetic field | 地磁场

The Earth behaves like a giant bar magnet. Its magnetic field lines emerge from the southern hemisphere, curve through space and enter the northern hemisphere.

地球就像一个巨大的条形磁铁。其磁力线从南半球发出，在空间中弯曲后进入北半球。

The Earth’s magnetic field lines point downwards and into the ground in the northern hemisphere. A compass north pole points towards geographic north because it is attracted by a magnetic south pole located near the geographic north pole.

北半球的地磁磁力线向下进入地面。指南针的 N 极指向地理北方，因为它受到位于地理北极附近的地磁南极吸引。

The angle between the Earth’s magnetic field and the horizontal is called the angle of dip. At the magnetic poles the dip angle is 90°, and at the magnetic equator it is 0°.

地磁场与水平面之间的夹角称为磁倾角。在地磁两极，磁倾角为 90°；在地磁赤道，磁倾角为 0°。

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