📚 IB Physics: Electric Fields & Magnetic Fields (SL/HL) | IB 物理：电场与磁场专题（含HL）
Electric and magnetic fields are central to the IB Physics syllabus, appearing in both SL and HL papers. They explain how charges interact at a distance, control the motion of particles, and power devices from capacitors to generators. This revision article consolidates the definitions, laws and exam-style applications you need, with HL extensions clearly labelled.
电场与磁场是 IB 物理考纲中的核心板块，在 SL 与 HL 试卷中均反复出现。它们解释了电荷如何在距离上相互作用、支配带电粒子的运动，并驱动从电容器到发电机的各类器件。本复习文章系统梳理关键定义、定律与考试常见应用，其中 HL 拓展内容均明确标注。
1. Electric Field Basics | 电场基础概念
An electric field exists in any region of space where a charged object experiences an electric force. The electric field strength E at a point is defined as the force per unit positive charge placed at that point:
E = F / q
where F is the electric force on a small positive test charge q. The SI unit is N·C⁻¹, which is equivalent to V·m⁻¹. Because E is a vector, its direction is the direction of the force on a positive test charge. Field lines start on positive charges and end on negative charges; the tangent to a field line gives the direction of E, and the line density indicates the field strength.
电场存在于空间中任何带电物体受到电场力的区域。电场强度 E 定义为该点处单位正电荷所受的力：
E = F / q
其中 F 是施加在小型正检验电荷 q 上的电场力。SI 单位为 N·C⁻¹，等效于 V·m⁻¹。由于 E 是矢量，其方向与正检验电荷所受力的方向一致。电场线从正电荷出发，终止于负电荷；电场线的切线方向表示 E 的方向，电场线的疏密程度表示电场的强弱。
- For an isolated point charge Q: E = kQ/r², radially outward for Q > 0 and inward for Q < 0. 单个点电荷 Q 的场强：E = kQ/r²，Q > 0 时沿径向向外，Q < 0 时沿径向向内。
- For a uniform field between parallel plates separated by distance d: E = V/d, where V is the potential difference. 平行板间匀强电场：E = V/d，其中 V 为两极板间的电势差。
2. Coulomb’s Law & Superposition | 库仑定律与叠加原理
Coulomb’s law gives the magnitude of the electrostatic force between two point charges q₁ and q₂ separated by a distance r in free space:
F = k q₁q₂ / r²
where k = 1/(4πε₀) ≈ 8.99 × 10⁹ N·m²·C⁻² and ε₀ is the permittivity of free space. The force is attractive when the charges have opposite signs and repulsive when they have the same sign. Since force is a vector, the net force on a charge due to several other charges is found by vector addition, a principle called superposition.
库仑定律给出了真空中两个点电荷 q₁ 与 q₂ 相距 r 时静电力的大小：
F = k q₁q₂ / r²
其中 k = 1/(4πε₀) ≈ 8.99 × 10⁹ N·m²·C⁻²，ε₀ 为真空介电常数。两电荷异号时力为引力，同号时为斥力。由于力是矢量，某电荷所受多个电荷的合力需用矢量加法求得，这一原理称为叠加原理。
- Common IB mistakes: forgetting that the denominator uses r² (not r), or dropping the sign of the charges when determining direction. 常见IB错误：忘记分母为 r²（而非 r），或在判断方向时忽略电荷的正负号。
- The field strength of a point charge follows directly from Coulomb’s law: E = F/q = kQ/r². 点电荷的场强可由库仑定律直接得出：E = F/q = kQ/r²。
3. Electric Potential & 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, with 1 V = 1 J·C⁻¹. For a point charge Q, the potential is V = kQ/r, where the sign of Q is included. The electric potential energy of a charge q placed at that point is Eₚ = qV.
电势 V 定义为将正检验电荷从无穷远处移至某点过程中，单位电荷所做的功。电势是标量，单位为伏特，1 V = 1 J·C⁻¹。对于点电荷 Q，电势为 V = kQ/r，计算时需包含 Q 的正负号。电荷 q 在该点的电势能为 Eₚ = qV。
Moving a charge between two points changes its potential energy by ΔEₚ = qΔV, and the work done by the electric field is W = −qΔV. Equipotential surfaces are always perpendicular to electric field lines, and no work is done when a charge moves along an equipotential. In a uniform field, the potential changes linearly with distance: E = |ΔV|/d.
将电荷从一点移至另一点，其电势能变化为 ΔEₚ = qΔV，电场力做功为 W = −qΔV。等势面始终与电场线垂直，电荷沿等势面移动时电场力不做功。在匀强电场中，电势随距离线性变化：E = |ΔV|/d。
4. Motion of Charged Particles in Electric Fields | 带电粒子在电场中的运动
A charged particle in a uniform electric field experiences a constant force F = qE and hence a constant acceleration a = qE/m. If the initial velocity is parallel to the field, the particle accelerates or decelerates in a straight line, and the kinetic energy change satisfies ΔEₖ = qΔV. If the initial velocity is perpendicular to the field, the trajectory is parabolic — exactly analogous to projectile motion under gravity.
带电粒子在匀强电场中受到恒力 F = qE，因而具有恒定加速度 a = qE/m。若初速度与电场平行，粒子做直线匀加速或匀减速运动，动能变化满足 ΔEₖ = qΔV。若初速度垂直于电场，其轨迹为抛物线——与重力下的抛体运动完全类似。
- Horizontal component of velocity stays constant; vertical component changes uniformly with time. 速度的水平分量保持不变，竖直分量随时间均匀变化。
- Application: in the Millikan oil-drop experiment, an electric force qE
Published by TutorHao | IB Physics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导Cancel reply