麥克斯韋方程組
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麥克斯韋方程組 Maxwell's Equations | |
歌曲封面 | |
演唱 | Isaak Wolf |
作詞 | Murasaki Hiroshi |
作曲 | Isaak Wolf |
視頻 | Isaak Wolf |
《麥克斯韋方程組》(英語:Maxwell's Equations)是虛擬YouTuber村崎博(Murasaki Hiroshi)作詞、Isaak Wolf作曲並演唱的原創歌曲,2022年8月18日發佈於bilibili、YouTube等平臺。
簡介
“ | This song is about Maxwell Equations, expressed in static and non-stationary situations, in vacuum or in the matter. This song explains what Maxwell's equations say, I wanted to create a tool to remember every equation. An educational song.
這首歌圍繞麥克斯韋方程組,描述其在靜態和非靜態的情況下,在真空和介質中的表達。這首歌解釋了麥克斯韋方程組的含義,我想創造一個工具來輔助每一個方程式的記憶。一首以教育為目的的歌曲。 |
” |
——村崎博 |
真空中
$\left\{ \begin{array}{c} \nabla \cdot \mathbf{E} = \frac {\rho} {\varepsilon_0} \\ \nabla \cdot \mathbf{B} = 0 \\ \nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}} {\partial t} \\ \nabla \times \mathbf{B} = \mu_0\mathbf{J} + \mu_0 \varepsilon_0 \frac{\partial \mathbf{E}} {\partial t} \end{array} \right.$
介質中
$\left\{ \begin{array}{c} \nabla \cdot \mathbf{D} = \rho_f \\ \nabla \cdot \mathbf{B} = 0 \\ \nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}} {\partial t} \\ \nabla \times \mathbf{H} = \mathbf{J}_f + \frac{\partial \mathbf{D}} {\partial t} \end{array} \right.$
歌曲
寬屏模式顯示視頻
歌詞
本段落中所使用的歌詞,其著作權屬於原著作權人,僅以介紹為目的引用。
I have no shirt tonight
今晚我褪去衣衫
Because I want to show you
因為我想為你展示
A set of 4 beautiful equations
一組四個美麗的方程式
They describe the world's most beautiful side.
它們描繪了世界最美的一面
Current, Waves and Light
電流、波和光
electromagnetism
電磁學
Come here, look at them
過來,看看它們
They are here on my chest
它們就在我的胸前
so close to my heart
如此貼近我的心臟
just like you, I'm going to tell you tonight
就像你一樣,今夜我將為你講述
About the waves and light.
波與光的奧秘
Your exam is tomorrow
你的考試就在明天
don't worry, we'll study until dawn
不要擔心,我們會學習到天亮
close like nucleons
像核子一般依偎
We start with the charge
我們從電荷開始
electrons and protons, equals and opposite:
電子和質子 (帶的電荷)大小相等而(電性)相反:
it's 1.6 at 10e-19 coulomb.
大小是1.6×10-19庫侖
Electromagnetic force is so intense
電磁力是如此強烈
sometimes it repulses, sometimes it attracts
它有時排斥,有時吸引
sometimes like you and me, we turn around
有時就像你和我,我們轉身
Study the material for it to be found
研究物質來尋找它
The shorter the distance, the greater the attraction
距離越短,引力越大
K is 9 billion
K是90億[注 5]
The spankings I'll lay on your skin tonight
今晚你身上要挨我的打
while you repeat the Columbian force
當你重複承受庫侖力時
These equations describe how electricity and magnetism work
這些方程式描述了電和磁如何作用
Our feeling, interaction,
我們的感覺、互動
Our sight and sensation
我們的視覺、知覺
Our touch
我們的觸覺
Do you feel it
你感覺到了嗎
I can feel your charge, it's positive
我能感覺到你的電荷,非常確定/是正電荷[注 6]
My electron cloud is so attracted
我的電子云已被深深吸引
Say my name, call me Sensei.
叫我的名字,叫我老師
Let's begin our Hide'n'Seek game:
讓我們開始捉迷藏遊戲:
like charges in insulators' gap,
就像絕緣體間隙中的電荷一樣
try to reach me, come to the other side.
試着靠近我,到另一邊來
it's okay
不用害怕
You're finally here, close to my chest again,
你終於來了,再次靠近我的胸膛
Ready to start, tell'em slowly
準備開始,慢慢告訴他們
First: Gauss Law
首先是高斯定律
You surround me with your surface
你用你的曲面包覆着我
I'm your electric flux
我是你的電通量
the inner charge
內部的電荷
Maxwell's second equation says:
麥克斯韋第二方程式說:
the magnetic field is made by lines
磁場由場線構成
Closed lines from a pole to another
從一個磁極到另一個磁極的閉合場線
no sources, they'll always return
沒有場源,它們總是會返回
'cause in the end, B flux is always zero
因為最終B[注 7]的通量總是0
Hold me now, we can't be detached
現在抓緊我,我們不能分離
No monopoles
沒有磁單極子
3rd equation, it may change in form
第三個方程式,它可能會改變形式
If we have no magnetic field
如果我們沒有磁場
then E is irrotational
那麼E[注 8]是無旋的
So we can define it through a potential
所以我們可以用勢來定義它
this field is conservative
這個場是保守場
The result is zero again
結果又是0
Let's make it harder
讓我們增加些難度
You can make B vary
你可以讓B變化
The situation isn't static anymore!
情況不再是靜態的!
Here it comes: Faraday induction
它來了:法拉第效應
The last one it's also called the Ampere's law
最後一個也叫(麥克斯韋-)安培定律,
With static fields it's easy
在靜場下,它會很簡單
The Circulation of B
B的環量
is just permeability
就是磁導率
times concatenated currents, Locally is just J,
乘以連續電流,在局域就是J[注 9]
permeability again
的通量,又一次[注 10]
But if we vary
但是如果我們(讓電場)變化
We need to add one more thing
我們需要(在方程式中)再加一項
Maxwell found a way to include
麥克斯韋找到了一種方法去包含
time-varying electric fields
時變電場(的影響)
Adding the displacement current
增加位移電流(的一項)
locally it's just the variation in time of E.
在局域就是E隨時間的變化
Here we have our special laws, All unified
於是我們得到了這特殊的定律,包納一切
a symmetric coherent set
這對稱統一的一組
Maxwell's Equations
麥克斯韋方程組
Protons, electrons and light
質子、電子和光
They seem to be different
它們看起來似乎不同
but they are the same
但又是一樣的
did you know these electromagnetic waves
你知道嗎?電磁波
have the same speed of light
有和光相同的速度
and hence are the same
因此它們就是同一種東西