Electromagnetic Induction and Faraday's Law · 电磁感应与法拉第定律
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| electromagnetic induction/ɪˌlektrəʊməɡˈnetɪk ɪnˈdʌkʃn/ | 电磁感应 | diàn cí gǎn yìng |
| magnetic flux/mæɡˈnetɪk flʌks/ | 磁通量 | cí tōng liàng |
Wave a magnet near a coil — and make electricity
- Push a magnet in and out of a coil of wire and a current flows, with no battery at all.
- Moving the magnet generates a voltage — the reverse of the motor effect.
- This is electromagnetic induction 电磁感应, and it powers every generator on Earth.
- Every power station, from coal to wind, is really just spinning magnets near coils.
在线圈旁挥动磁铁——就发出了电
- 把磁铁在线圈里推进推出,就有电流流动,完全不用电池。
- 移动磁铁产生了电压——电动机效应的逆过程。
- 这就是电磁感应,它驱动着地球上每一台发电机。
- 每一座电站,从煤电到风电,其实都只是在线圈旁旋转的磁铁。
A changing field induces a voltage
- What matters is a change in the magnetic field through the coil — its flux 磁通量.
- A changing flux induces a voltage (an EMF) in the coil.
- Move the magnet, spin the coil, or switch a current on or off — any change works.
- Hold everything still and the induced voltage vanishes; it is the change that counts.
变化的场感应出电压
- 关键是穿过线圈的磁场的变化——它的磁通量。
- 变化的磁通量在线圈中感应出一个电压(电动势)。
- 移动磁铁、旋转线圈,或开关一个电流——任何变化都行。
- 让一切静止,感应电压就消失;起作用的是那个变化。
Induce a current · 感应电流
Move a magnet through a coil at different speeds and watch the induced current change. · 以不同速度移动磁铁穿过线圈，观察感应电流的变化。
What is needed to induce a voltage in a coil? · 要在线圈中感应出电压需要什么？
Only a changing flux induces an EMF; a steady field does nothing. · 只有变化的磁通量才能感应出电动势；恒定磁场不起作用。
Faraday's law
- Faraday's law: the induced EMF equals the rate of change of flux, $\varepsilon = -N\dfrac{\Delta\Phi}{\Delta t}$.
- $N$ is the number of turns, and $\Phi$ the magnetic flux through each.
- A faster change, or more turns, gives a bigger induced voltage.
- The minus sign is Lenz's law — the induced current opposes the change that made it.
法拉第定律
- 法拉第定律:感应电动势等于磁通量的变化率,$\varepsilon = -N\dfrac{\Delta\Phi}{\Delta t}$。
- $N$ 是匝数,$\Phi$ 是穿过每匝的磁通量。
- 更快的变化,或更多的匝数,给出更大的感应电压。
- 负号是楞次定律——感应电流反抗产生它的那个变化。
A $100$-turn coil has its flux change by $0.02\ \text{Wb}$ in · 入 $0.5\ \text{s}$. What is the size of the induced EMF, in $\text{V}$? · A $100$匝线圈的磁通量变化为 $0.02\ \text{Wb}$ ，在 $0.5\ \text{s}$内。感应电动势的大小为 $\text{V}$?
$|\varepsilon| = N\Delta\Phi/\Delta t = 100 \times 0.02/0.5 = 4\ \text{V}$.
Increasing the number of turns in the coil makes the induced EMF: · 增加线圈匝数会使感应电动势：
$\varepsilon = -N\Delta\Phi/\Delta t$: more turns $N$ gives a bigger EMF. · $\varepsilon = -N\Delta\Phi/\Delta t$：更多匝数$N$带来更大的电动势。
The minus sign in Faraday's law is ____ law: the induced current opposes the change. · 法拉第定律中的负号代表____定律：感应电流阻碍变化。
Lenz's law: the induced current opposes the change in flux that produced it. · 楞次定律：感应电流阻碍产生它的磁通量变化。
Generators and transformers
- A generator spins a coil in a field, constantly changing the flux to make AC electricity.
- A transformer uses a changing current in one coil to induce a voltage in another.
- Both are just Faraday's law at work, converting motion (or changing current) into voltage.
- Induction is the two-way bridge between electricity and magnetism.
发电机与变压器
- 发电机在场中旋转线圈,不断改变磁通量来产生交流电。
- 变压器用一个线圈中变化的电流,在另一个线圈中感应出电压。
- 两者都只是法拉第定律在起作用,把运动(或变化的电流)转化为电压。
- 感应是电与磁之间双向的桥梁。
A magnet held still inside a coil induces a steady current. · 将磁铁静止放在线圈内会产生恒定电流。
No change in flux means no induced current — the magnet must be moving. · 磁通量无变化意味着无感应电流——磁铁必须移动。
Select all · 所有 ways to increase the induced EMF in a coil. · 选择所有增大线圈感应电动势的方法。
A faster change, more turns, or a stronger magnet all raise the EMF. Holding still induces nothing. · 更快的变化、更多匝数或更强磁铁都会提高电动势。静止不动不会感应出任何电动势。
Induction needs a changing flux, not just a field. A magnet sitting still inside a coil induces no current — only moving it (changing the flux) does. And Lenz's law (the minus sign) means the induced current always opposes the change causing it.
感应需要变化的磁通量,而不只是一个场。静止不动放在线圈里的磁铁不感应出电流——只有移动它(改变磁通量)才行。而楞次定律(负号)意味着感应电流总是反抗引起它的那个变化。
A coil of $N = 100$ turns has the flux through it change by $\Delta\Phi = 0.02\ \text{Wb}$ in $\Delta t = 0.5\ \text{s}$. Find the size of the induced EMF.
- $|\varepsilon| = N\dfrac{\Delta\Phi}{\Delta t} = 100 \times \dfrac{0.02}{0.5} = 4\ \text{V}$.
Change the flux faster (smaller $\Delta t$) and the induced voltage grows.
一个 $N = 100$ 匝的线圈,穿过它的磁通量在 $\Delta t = 0.5\ \text{s}$ 内变化 $\Delta\Phi = 0.02\ \text{Wb}$。求感应电动势的大小。
- $|\varepsilon| = N\dfrac{\Delta\Phi}{\Delta t} = 100 \times \dfrac{0.02}{0.5} = 4\ \text{V}$。
让磁通量变化更快(更小的 $\Delta t$),感应电压就增大。
Electromagnetic induction: a changing magnetic flux induces an EMF. Faraday's law: $\varepsilon = -N\dfrac{\Delta\Phi}{\Delta t}$ — faster change or more turns means more voltage. The minus sign is Lenz's law (the induced current opposes the change). Generators and transformers all run on this.
电磁感应:变化的磁通量感应出电动势。法拉第定律:$\varepsilon = -N\dfrac{\Delta\Phi}{\Delta t}$——更快的变化或更多的匝数意味着更大的电压。负号是楞次定律(感应电流反抗变化)。发电机和变压器都靠它运行。