题型概述：Physics Bowl 电学与磁学Question types: Physics Bowl electricity & magnetism
Top在我们整理的 15 套真题里，电路 46 道、静电 34 道、磁学与电磁感应 33 道，合计 113 道（约 15%）。电路题最多，几乎每年都有一道"看图求电压/电流"；静电题常考场强方向与电势的正负。本模块选 5 道 2024–2025 年的题。In the 15 papers of our bank there are 46 circuits questions, 34 electrostatics and 33 magnetism and induction: 113 in all, about 15%. Circuits come up most, nearly every year with a "read the diagram, find a voltage or current" item; electrostatics likes the direction of the field and the sign of the potential. This module works five questions from 2024–2025.
1电路：先找"已知量最多"的元件Circuits: start where you know the most
串联电流相同、电压相加；并联电压相同、电流相加。解题时从已知两个量的元件出发（例如已知电阻和电流），用欧姆定律 V = IR 一步步向外推。电表只测它所在支路或所跨两点。Series: same current, voltages add. Parallel: same voltage, currents add. Start from the element where two quantities are known (say resistance and current) and work outwards with Ohm's law V = IR. A meter reads only its own branch, or only the two points it spans.
| 串联Series | 并联Parallel | |
|---|---|---|
| 相同的量Shared | I | V |
| 等效电阻Equivalent | R = R₁ + R₂ | 1/R = 1/R₁ + 1/R₂ |
| 功率比较用Compare power with | P = I²R | P = V²/R |
2静电：场强是矢量，电势是标量Electrostatics: field is a vector, potential a scalar
点电荷的场强 E = kq/r²，方向离开正电荷、指向负电荷；几个电荷的场强要按矢量相加。电势 V = kq/r 带正负号，直接代数相加。所以同一点上可以"场强不为零而电势为零"，也可以反过来。A point charge gives E = kq/r², pointing away from a positive charge and towards a negative one; fields from several charges add as vectors. Potential V = kq/r carries a sign and adds as plain numbers. So a point can have a non-zero field and zero potential, or the other way round.
3磁学：两根平行导线Magnetism: two parallel wires
同向电流相吸、反向电流相斥。每米导线受力 F/L = μ₀I₁I₂/(2πd)，μ₀ = 4π × 10⁻⁷ T·m/A，所以 μ₀/(2π) = 2 × 10⁻⁷。上方导线要被"托住"，下方导线的磁力必须向上，也就是两电流反向。Currents in the same direction attract; opposite currents repel. The force per metre is F/L = μ₀I₁I₂/(2πd) with μ₀ = 4π × 10⁻⁷ T·m/A, so μ₀/(2π) = 2 × 10⁻⁷. For a lower wire to hold an upper wire up, the magnetic force must point up: the currents must be opposite.
4本模块的 5 道题The five questions in this module
| 题型Type | 核心一步Core step | 真题Paper |
|---|---|---|
| 串并联求电源电压Supply voltage of a series-parallel circuit | 从已知电流的支路出发Start from the branch with the known current | 2025 Q22 |
| 并联电阻的功率比Power ratio of parallel resistors | P = V²/R | 2025 Q46 |
| 等量异号电荷中点Midpoint of a ±q pair | 场强矢量和、电势代数和Vector sum for E, plain sum for V | 2025 Q49 |
| 并联支路中的电流表Ammeter in one parallel branch | 支路电压 = 电源电压Branch voltage = supply voltage | 2024 Q35 |
| 导线磁悬浮Magnetic levitation of a wire | μ₀I₁I₂L/(2πd) = mg | 2024 Q49 |