Electric Fields and Magnetic Fields | 电场与磁场

📚 Electric Fields and Magnetic Fields | 电场与磁场

In IB Physics, electric and magnetic fields are fundamental concepts that explain how charges interact without direct contact. This article provides a structured comparison of these two fields, highlighting key definitions, formulas, and exam strategies.

在IB物理中，电场与磁场是解释电荷之间无需直接接触便能相互作用的基本概念。本文将对这两种场进行系统比较，重点介绍关键定义、公式和考试策略。

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1. Electric Field Basics | 电场的基本性质

An electric field exists in the region around a charged object. It exerts a force on other charges placed within it. The field is a vector quantity, defined as force per unit positive test charge.

电场存在于带电物体周围的空间区域，会对置于其中的其他电荷施加作用力。电场是矢量，定义为每单位正检验电荷所受的力。

• Direction: away from positive charges, toward negative charges.

  方向：正电荷向外，负电荷指向内。

• Units: N/C or equivalently V/m.

  单位：N/C，等价于 V/m。

• Test charge must be small and positive to avoid disturbing the original field.

  检验电荷必须足够小且带正电，以免干扰原有电场分布。

E = F / q

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2. Coulomb’s Law and Electric Field Strength | 库仑定律与电场强度

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

库仑定律描述两个点电荷之间的静电力大小，与电荷量乘积成正比，与距离的平方成反比。

F = k · q₁q₂ / r² , k = 8.99 × 10⁹ N·m²/C²

The electric field strength due to a point charge Q at a distance r is derived from Coulomb’s law:

由库仑定律可导出点电荷Q在距离r处产生的电场强度：

E = kQ / r²

For multiple charges, the net field is the vector sum of individual fields.

对于多个电荷，合场强为各场强的矢量叠加。

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

Electric potential V is the potential energy per unit charge at a point in an electric field. It is a scalar quantity, making it easier to combine than electric field.

电势V是电场中某一点处的电势能除以检验电荷的电荷量，是标量，因此叠加比电场矢量更方便。

V = U / q = kQ / r

Work done to move a charge through a potential difference is given by W = qΔV. Along an equipotential surface, no work is done because the potential is constant.

移动电荷经过电势差所做的功为 W = qΔV。沿等势面移动电荷时，电势不变，做功为零。

• Units: volt (V), 1 V = 1 J/C.

  单位：伏特（V），1 V = 1 J/C。

• Positive charges move from high to low potential; negative charges do the opposite.

  正电荷从高电势移向低电势，负电荷则相反。

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4. Field Lines and Equipotentials | 电场线与等势面

Electric field lines are used to visualize the field. They begin on positive charges and end on negative charges. The density of lines represents the field strength.

电场线用于可视化电场分布，始于正电荷，终于负电荷。电场线的疏密表示场强大小。

• Field lines never cross; the tangent at any point gives the field direction.

  电场线不相交，某点的切线方向即为该点场强方向。

• Equipotential lines are always perpendicular to field lines.

  等势线始终与电场线垂直。

• Moving a charge along an equipotential line requires zero work.

  电荷沿等势线移动时做功为零。

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5. Sources and Representation of Magnetic Fields | 磁场的来源与表示

Magnetic fields are produced by permanent magnets and by moving electric charges (currents). Unlike electric field lines, magnetic field lines form continuous closed loops.

磁场由永磁体及运动电荷（电流）产生。与电场线不同，磁感线是闭合的连续环。

Outside a magnet, field lines point from the north pole to the south pole; inside the magnet, they continue from south to north.

在磁体外部，磁感线从北极到南极；在磁体内部，则从南极回到北极。

• Magnetic field strength is denoted by B, measured in teslas (T).

  磁感应强度用B表示，单位为特斯拉（T）。

• 1 T = 1 N/(A·m).

  1 T = 1 N/(A·m)。

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6. Magnetic Force on Moving Charges | 磁场对运动电荷的作用力

A charged particle moving through a magnetic field experiences a force perpendicular to both its velocity and the magnetic field. This is the Lorentz force.

带电粒子在磁场中运动时将受到既垂直于速度又垂直于磁场方向的力，即洛伦兹力。

F = qvB sinθ

When θ = 90°, the particle moves in a circular path with radius r = mv/(qB). Since the force is always perpendicular to velocity, it does no work and kinetic energy remains constant.

当 θ = 90° 时，粒子做圆周运动，半径 r = mv/(qB)。因为洛伦兹力始终垂直于速度，所以不做功，动能保持不变。

• Use the right-hand rule: fingers point in direction of v, curl toward B, thumb points to F for a positive charge.

  使用右手定则：右手四指指向速度v方向，向磁场B方向弯曲，拇指指向正电荷受力的方向。

• For a negative charge, the force direction is opposite.

  对于负电荷，受力方向相反。

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7. Magnetic Force on Current-Carrying Wires | 载流导线在磁场中的受力

A wire carrying current I in a magnetic field B experiences a force given by:

置于磁场B中的载流导线（电流为I）所受安培力为：

F = BIL sinθ

Here L is the length of the wire inside the field, and θ is the angle between the current direction and the magnetic field. This principle is the basis of electric motors.

其中L为导线在磁场中的长度，θ为电流方向与磁场方向的夹角。该原理是电动机工作的基础。

• Two parallel wires carrying currents in the same direction attract; opposite currents repel.

  两条平行导线通以同向电流时相互吸引，反向电流则相互排斥。

• The direction of F is again determined by the right-hand rule (or Fleming’s left-hand rule).

  安培力方向同样由右手定则（或左手定则）确定。

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8. Electromagnetic Induction | 电磁感应

When magnetic flux through a circuit changes, an electromotive force (EMF) is induced. This is Faraday’s law of induction.

当穿过回路的磁通量发生变化时，回路中会产生电动势，这就是法拉第电磁感应定律。

ε = −N ΔΦ / Δt

The negative sign reflects Lenz’s law: the induced current opposes the change in flux.

负号体现了楞次定律：感应电流的方向总是阻碍引起感应电流的磁通量变化。

• Magnetic flux Φ = BA cosθ, where θ is the angle between B and the normal to the area.

  磁通量 Φ = BA cosθ，其中θ为磁感应强度B与面积法线方向的夹角。

• Flux linkage NΦ is used for a coil with N turns.

  对N匝线圈，使用磁链NΦ。

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9. Comparing Electric and Magnetic Fields | 电场与磁场的对比

The table below summarises the key similarities and differences between electric and magnetic fields.

下表总结了电场与磁场之间的主要异同点。

Property | 性质	Electric Field | 电场	Magnetic Field | 磁场
Source | 源	Static charges | 静止电荷	Moving charges / magnets | 运动电荷/磁体
Force on charge | 对电荷的力	F = qE (any charge, any motion) | 适用于任何电荷	F = qvB sinθ (only moving charges) | 只对运动电荷
Work done | 做功	Can do work, changes kinetic energy | 可以做功，改变动能	Always zero work (force ⊥ velocity) | 总做功为零
Field lines | 场线	Start on +, end on − | 起于正电荷，终于负电荷	Closed loops | 闭合曲线
Quantity type | 物理量类型	Vector (E) and scalar (V) | 矢量（E）与标量（V）	Vector (B) | 矢量（B）

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10. Problem-Solving Strategies and Common Exam Points | 解题策略与常见考点

In IB Physics exams, questions on fields often combine conceptual understanding with vector calculations. The following strategies help maximise marks.

IB物理考试中的场论题通常结合概念理解与矢量计算，以下策略有助于获得高分。

• Always draw a diagram first. Identify the directions of E, B, v, and F clearly.

  首先画示意图，清晰标出E、B、v和F的方向。

• For electric fields, separate the idea of field force from potential energy; they are closely related but distinct.

  对于电场，要区分电场力与电势能；两者密切相关但不相同。

• When using F = qvB, check the angle θ; do not forget sinθ equals 1 for perpendicular motion.

  使用F = qvB时，注意检查角度θ；垂直运动时sinθ=1。

• Apply right-hand rules consistently. Practise them in both electric and magnetic contexts.

  持续练习右手定则，并在电场与磁场情境中正确运用。

• Remember that magnetic force never changes the speed of a particle; it only changes direction.

  牢记洛伦兹力不会改变粒子的速率，只改变方向。

Common mistakes: confusing gravitational and electric fields, omitting vector signs, or mixing up the units of B and E.

常见错误：混淆引力场与电场、遗漏矢量符号、或弄混B和E的单位。

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