HKDSE Physics Elective
Chapter 5: Electromagnetic Induction | 電磁感應
Billy Sir’s Smart Notes: Master Faraday’s Law, Lenz’s Law, Generators, and Eddy Currents.
由中大物理系碩士 Billy Sir 編寫，助你極速掌握法拉第定律、楞次定律、發電機及渦電流。
1. Magnetic Flux | 磁通量
Magnetic flux is a measure of the total magnetic field passing through a given area. 磁通量是穿過給定面積的總磁場的量度。
🧲 Formula for Magnetic Flux | 磁通量公式
- \( \Phi \): Magnetic flux in Webers (Wb) (磁通量，單位：韋伯)
- \( B \): Magnetic field strength in Tesla (T) (磁場強度，單位：特斯拉)
- \( A \): Area of the coil in \( m^2 \) (線圈面積)
- \( \theta \): Angle between the magnetic field and the normal (perpendicular) to the area. (磁場與面積法線之間的夾角)
2. Faraday’s Law & Wire Cutting | 法拉第定律與導線切割磁場
Electromagnetic induction occurs when there is a change in magnetic flux linking a circuit, producing an induced e.m.f. (electromotive force). 當連接電路的磁通量發生變化時，會產生感生電動勢，這就是電磁感應。
| Concept (概念) | Formula (公式) | Description (描述) |
|---|---|---|
| Faraday’s Law 法拉第定律 |
$$ \varepsilon = -N \frac{\Delta \Phi}{\Delta t} $$ | The induced e.m.f. is directly proportional to the rate of change of magnetic flux linkage. (感生電動勢與磁通量匝數的變化率成正比。) |
| Wire Cutting Field 導線切割磁場 |
$$ \varepsilon = B l v $$ | Induced e.m.f. when a straight wire of length \( l \) moves at velocity \( v \) perpendicularly through a magnetic field \( B \). (長度為 \( l \) 的直導線以速度 \( v \) 垂直切割磁場 \( B \) 時產生的感生電動勢。) |
3. Lenz’s Law | 楞次定律
Lenz’s Law states that the direction of the induced e.m.f. (and hence induced current) is always such as to oppose the change producing it. This is a consequence of the conservation of energy. 楞次定律指出，感生電動勢（及感生電流）的方向總是反抗引起它的變化。這是能量守恆的結果。
🎯 Examples of Lenz’s Law | 楞次定律例子
- Pushing a North pole into a coil: The end of the coil facing the magnet becomes a North pole to repel the magnet. Work must be done against this repulsion. (將北極推入線圈：線圈面向磁鐵的一端變成北極以排斥磁鐵。必須克服此排斥力作功。)
- Pulling a North pole out of a coil: The end of the coil facing the magnet becomes a South pole to attract the magnet, opposing its withdrawal. (將北極拉出線圈：線圈面向磁鐵的一端變成南極以吸引磁鐵，反抗其離開。)
4. Generators | 發電機
A generator converts mechanical energy into electrical energy by rotating a coil in a magnetic field. 發電機通過在磁場中旋轉線圈，將機械能轉化為電能。
⚡ AC Generator | 交流發電機
Uses slip rings to connect the rotating coil to the external circuit. The output is an alternating current (AC) that varies sinusoidally. (使用滑環將旋轉線圈連接到外部電路。輸出為呈正弦變化的交流電。)
Note: To make a DC generator, a split-ring commutator is used instead of slip rings, producing a pulsating direct current. (註：若要製造直流發電機，需使用換向器代替滑環，產生脈動直流電。)
5. Eddy Currents & Applications | 渦電流及其應用
When a solid piece of metal experiences a changing magnetic field, localized circular currents called eddy currents are induced within the metal. 當整塊金屬處於變化的磁場中時，金屬內部會產生局部的環形電流，稱為渦電流。
| Application (應用) | How it works (運作原理) |
|---|---|
| Induction Cooker 電磁爐 |
An alternating current in the cooker’s coil produces a rapidly changing magnetic field. This induces large eddy currents in the metal pot above it. The electrical resistance of the pot causes it to heat up rapidly (\( P = I^2R \)). (爐內線圈的交流電產生快速變化的磁場，在金屬鍋底感生出巨大的渦電流。鍋的電阻使其迅速發熱。) |
| Search Coil 探測線圈 |
A small coil used to measure varying magnetic fields. When placed in an AC magnetic field, an e.m.f. is induced in the search coil, which can be measured using a CRO (oscilloscope) or a data logger. (用於測量變化磁場的小線圈。置於交流磁場中時，會感生出電動勢，可用示波器或數據收集器測量。) |
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