IB Physics: Core Concepts of Electric and Magnetic Fields | IB物理：电场与磁场的核心概念

📚 IB Physics: Core Concepts of Electric and Magnetic Fields | IB物理：电场与磁场的核心概念

Electric and magnetic fields form one of the most fundamental pillars of the IB Physics syllabus. From Coulomb’s law to the motion of charged particles in magnetic fields, these concepts explain everything from why a balloon sticks to a wall to how particle accelerators work. This revision guide consolidates the key definitions, equations, and relationships you need for your exams.

电场与磁场是IB物理课程中最基础的支柱之一。从库仑定律到带电粒子在磁场中的运动，这些概念解释了从气球吸附在墙上到粒子加速器如何工作的各种现象。本复习指南整合了你考试所需的关键定义、方程和关系。

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1. The Concept of an Electric Field | 电场的概念

An electric field is a region of space around a charged object where another charged object experiences a force. It is a vector field, meaning it has both magnitude and direction at every point in space. The electric field strength E at a point is defined as the force per unit positive charge placed at that point:

电场是电荷周围存在的一个空间区域，在该区域内另一带电物体会受到力的作用。电场是矢量场，意味着它在空间每一点都有大小和方向。某一点的电场强度E定义为放置在该点的单位正电荷所受的力：

E = F / q

Where F is the force in newtons (N) and q is the test charge in coulombs (C). The SI unit of electric field strength is N C⁻¹, which is equivalent to V m⁻¹.

其中F是力，单位为牛顿（N），q是试探电荷，单位为库仑（C）。电场强度的国际单位是N C⁻¹，与V m⁻¹等价。

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2. Coulomb’s Law | 库仑定律

Coulomb’s law describes the electrostatic force between two point charges. The magnitude of the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them:

库仑定律描述了两个点电荷之间的静电力。力的大小与电荷量的乘积成正比，与它们之间距离的平方成反比：

F = k |q₁q₂| / r²

Here, k is Coulomb’s constant, equal to 8.99 × 10⁹ N m² C⁻². In IB Physics, we often write this in terms of the permittivity of free space ε₀, where k = 1/(4πε₀). The force is attractive for opposite charges and repulsive for like charges. This is an inverse square law, meaning that doubling the distance reduces the force to one quarter of its original value.

其中k是库仑常数，等于8.99 × 10⁹ N m² C⁻²。在IB物理中，我们通常用真空介电常数ε₀来表示，即k = 1/(4πε₀)。异种电荷之间力为引力，同种电荷之间力为斥力。这是一个平方反比定律，意味着距离加倍时，力减小到原来的四分之一。

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3. Electric Field of a Point Charge | 点电荷的电场

For a point charge Q, the electric field strength at a distance r can be derived directly from Coulomb’s law. Combining E = F/q with F = kQq/r² gives:

对于点电荷Q，距离r处的电场强度可以直接从库仑定律推导出来。将E = F/q与F = kQq/r²结合，得到：

E = kQ / r²

The direction of the field is radially outward from a positive charge and radially inward toward a negative charge. Note that the field strength decreases with the square of the distance — this is a key concept for sketching field patterns and solving problems involving multiple charges.

电场方向从正电荷径向向外，指向负电荷径向向内。注意电场强度随距离的平方而减小——这是描绘电场线和解决多电荷问题时的关键概念。

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4. Electric Field Lines | 电场线

Electric field lines provide a visual representation of the electric field. The rules for drawing them are:

电场线为电场提供了直观的视觉表示。绘制电场线的规则如下：

• Field lines start on positive charges and end on negative charges (or at infinity).
• 电场线从正电荷出发，终止于负电荷（或无穷远处）。
• The tangent to a field line at any point gives the direction of the force on a positive test charge.
• 电场线上任意一点的切线方向表示正试探电荷在该点所受力的方向。
• The density of field lines indicates the magnitude of the field — closer lines mean a stronger field.
• 电场线的疏密表示电场强度的大小——线越密，场越强。
• Field lines never cross each other.
• 电场线永不相交。

Between two parallel plates with opposite charges, the field lines are parallel and equally spaced, creating a uniform electric field. In this region, the force on a charge is constant in magnitude and direction.

在两块带异种电荷的平行板之间，电场线平行且等距，形成匀强电场。在该区域内，电荷所受的力大小和方向恒定。

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5. Electric Potential and Potential Energy | 电势与电势能

Electric potential V at a point is the work done per unit charge in bringing a positive test charge from infinity to that point. It is a scalar quantity measured in volts (V), where 1 V = 1 J C⁻¹. For a point charge Q:

某一点的电势V是将正试探电荷从无穷远处移到该点所做的功除以电荷量。它是标量，单位为伏特（V），其中1 V = 1 J C⁻¹。对于点电荷Q：

V = kQ / r

The electric potential energy of a charge q at a point is then simply U = qV. The potential difference between two points, ΔV, is equal to the work done per unit charge in moving a charge between those points. In a uniform field, the relationship between potential difference and field strength is ΔV = Ed, where d is the distance parallel to the field direction.

电荷q在某一点的电势能即为U = qV。两点之间的电势差ΔV等于将单位电荷在两点之间移动所做的功。在匀强电场中，电势差与场强的关系为ΔV = Ed，其中d是沿场方向的距离。

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6. The Concept of a Magnetic Field | 磁场的概念

A magnetic field is a region of space where a moving charge or a magnetic dipole experiences a force. Magnetic fields are produced by moving charges — that is, by electric currents. The magnetic field strength, also called magnetic flux density, is denoted by B and measured in tesla (T). One tesla equals one newton per ampere per meter (N A⁻¹ m⁻¹).

磁场是运动电荷或磁偶极子受到力的作用的空间区域。磁场由运动的电荷产生，也就是由电流产生。磁感应强度（也称磁通量密度）用B表示，单位为特斯拉（T）。1特斯拉等于1牛顿每安培每米（N A⁻¹ m⁻¹）。

The direction of a magnetic field is conventionally the direction in which the north pole of a compass needle points. Magnetic field lines run from a north pole to a south pole outside the magnet, and they form closed loops through the interior of the magnet.

磁场的方向习惯上定义为指南针北极指向的方向。在磁体外部，磁感线从北极指向南极，并通过磁体内部形成闭合回路。

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7. Force on a Moving Charge in a Magnetic Field | 磁场中运动电荷所受的力

A charged particle moving with velocity v in a magnetic field B experiences a force described by the equation:

在磁场B中以速度v运动的带电粒子所受的力由以下方程描述：

F = qvB sin θ

Where q is the charge and θ is the angle between the velocity and the magnetic field direction. The direction of this force is always perpendicular to both the velocity and the magnetic field, given by Fleming’s left-hand rule. If θ = 90°, the particle moves in a circular path because the magnetic force acts as a centripetal force:

其中q是电荷量，θ是速度方向与磁场方向之间的夹角。该力的方向始终垂直于速度和磁场方向，由左手定则确定。当θ = 90°时，粒子做圆周运动，因为磁场力充当向心力：

qvB = mv² / r

This leads to the radius of the circular path r = mv/(qB). If the velocity has a component parallel to the field, the particle follows a helical path.

由此可得圆周运动的半径r = mv/(qB)。如果速度有平行于磁场的分量，粒子将沿螺旋路径运动。

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8. Force on a Current-Carrying Wire | 电流导体所受的安培力

A current-carrying conductor placed in a magnetic field also experiences a force. For a wire of length L carrying current I perpendicular to the magnetic field B, the magnitude of the force is:

放置于磁场中的载流导体也会受到力的作用。对于长度为L、电流为I且垂直于磁场B的导线，力的大小为：

F = BIL

More generally, when the angle between the wire and the field is θ, F = BIL sin θ. This principle is the basis of the electric motor — a current-carrying coil in a magnetic field experiences a torque that causes it to rotate.

更一般地，当导线与磁场的夹角为θ时，F = BIL sin θ。这一原理是电动机的基础——磁场中的载流线圈受到力矩作用而转动。

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9. Magnetic Field of a Long Straight Wire | 长直导线的磁场

A long straight wire carrying current I produces a magnetic field whose field lines form concentric circles around the wire. The magnitude of the field at a distance r from the wire is:

载流I的长直导线产生的磁场，其磁感线环绕导线形成同心圆。距离导线r处的磁感应强度大小为：

B = μ₀I / (2πr)

Here, μ₀ is the permeability of free space, equal to 4π × 10⁻⁷ T m A⁻¹. The direction of the field is given by the right-hand grip rule: if you grip the wire with your right hand with the thumb pointing in the direction of the current, your fingers curl in the direction of the field lines.

其中μ₀是真空磁导率，等于4π × 10⁻⁷ T m A⁻¹。磁场方向由右手螺旋定则确定：右手握住导线，拇指指向电流方向，四指弯曲的方向即为磁感线方向。

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10. Comparison: Electric Fields vs Magnetic Fields | 电场与磁场的对比

Understanding the similarities and differences between electric and magnetic fields is essential for constructing clear mental models. The table below summarizes the key comparisons:

理解电场与磁场的异同对于构建清晰的物理模型至关重要。下表总结了关键的对比：

Property | 性质	Electric Field | 电场	Magnetic Field | 磁场
Source | 源	Stationary charges | 静止电荷	Moving charges / currents | 运动电荷/电流
Force on a charge | 对电荷的作用	Acts on stationary and moving charges | 对静止和运动电荷均起作用	Acts only on moving charges | 仅对运动电荷起作用
Force direction | 力的方向	Parallel or anti-parallel to field | 平行或反平行于场方向	Perpendicular to both velocity and field | 垂直于速度和场方向
Work done | 做功	Force can do work, changing kinetic energy | 力可以做功，改变动能	Force does no work — only changes direction | 力不做功——只改变方向
Field lines | 场线	Start and end on charges | 始于电荷，止于电荷	Form closed loops | 形成闭合回路

A crucial consequence of the magnetic force doing no work is that a magnetic field can never change the speed of a charged particle — it can only change its direction. In contrast, an electric field can accelerate or decelerate particles, changing their kinetic energy.

磁场力不做功这一关键推论意味着磁场永远不能改变带电粒子的速率——它只能改变其方向。相比之下，电场可以加速或减速粒子，改变其动能。

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11. Electromagnetic Induction | 电磁感应

Electromagnetic induction is the phenomenon where a changing magnetic field induces an electromotive force (EMF) in a conductor. Faraday’s law states that the induced EMF is equal to the negative rate of change of magnetic flux linkage:

电磁感应是指变化的磁场在导体中感应出电动势（EMF）的现象。法拉第定律表明，感应电动势等于磁通量变化率的负值：

ε = −N (ΔΦ / Δt)

Where N is the number of turns in the coil, ΔΦ is the change in magnetic flux (Φ = BA cos θ), and Δt is the time interval. Lenz’s law, which explains the negative sign, states that the induced current flows in a direction such that its magnetic field opposes the change that produced it. This is a direct consequence of the conservation of energy.

其中N是线圈匝数，ΔΦ是磁通量的变化量（Φ = BA cos θ），Δt是时间间隔。楞次定律解释了负号的物理意义：感应电流的方向使得其产生的磁场阻碍引起它的磁通量变化。这是能量守恒的直接结果。

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12. Exam Tips and Common Pitfalls | 考试技巧与常见误区

To succeed in IB Physics exam questions on this topic, keep these points in mind:

要在IB物理考试中答好这类题目，请牢记以下几点：

• Always draw field line diagrams carefully — examiners look for arrows indicating direction and correct line density.
• 始终仔细绘制场线图——考官会检查表示方向的箭头和线的疏密是否正确。
• Convert units before substituting into equations. Remember that cm must become m, and µC must become C.
• 在代入方程前统一单位。记住厘米必须换算为米，微库仑必须换算为库仑。
• For magnetic force problems, first identify whether the charge moves parallel, perpendicular, or at an angle to the field.
• 对于磁场力问题，首先判断电荷的运动方向与磁场是平行、垂直还是成一定角度。
• Do not confuse the formulas for electric potential (V = kQ/r) and electric field (E = kQ/r²) — one falls off as 1/r, the other as 1/r².
• 不要混淆电势公式（V = kQ/r）和电场强度公式（E = kQ/r²）——一个随1/r变化，另一个随1/r²变化。
• When using Fleming’s left-hand rule, remember the order: Force (thumb), magnetic Field (index finger), Current (middle finger).
• 使用左手定则时，记住顺序：力（拇指）、磁场（食指）、电流（中指）。

Mastering electric and magnetic fields requires practice with both qualitative diagrams and quantitative calculations. Build a solid foundation by drawing field patterns, deriving key relationships, and working through past paper questions systematically.

掌握电场和磁场需要同时练习定性作图和定量计算。通过绘制场图、推导关键关系以及系统性地练习历年真题来打好坚实基础。

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