Into Unscientific

Students who have lived from BC to the present should know it.

A long time ago, it was discovered that there are forces between electric charges and between magnets.

But initially, the two effects were not linked.

Until people discovered that some stones struck by lightning were magnetic, they guessed that there might be some relationship between electricity and magnetism.

The rest of the story is very simple.

Oersted discovered that electricity can produce magnetism, and Faraday discovered that magnetism can produce electricity.

People finally realized that the relationship between electricity and magnetism is inseparable, and began to use magnets to make generators and electric currents to make electromagnets.

But it was mentioned before.

Although Faraday discovered the phenomenon of electromagnetic induction, and expressed the lines of magnetic induction with magnet shavings.

But it was Newman and Weber who also appeared in the classroom today who finally summed up the law of electromagnetic induction.

It was only in honor of Faraday's contribution that they named this formula Faraday's law of electromagnetic induction.

The derivation process of Newman and Weber involves the Newman vector potential An and the Weber vector Aw, which are relatively complicated, and will not be explained in detail here.

all in all.

The final formula of Faraday's law of electromagnetic induction is as follows:

1. E=nΔΦ/t

(1) When the change of magnetic flux is caused by the change of area, ΔΦ=BΔS, then E=nBΔS/t;

(2) When the change of magnetic flux is caused by the change of magnetic field, ΔΦ=ΔBS, then E=nΔBS/t;

(3) The change of the magnetic flux is caused by the change of the area and the magnetic field, then according to the definition, ΔΦ=|Φend-Φbegin|,

2. When the conductor bar cuts the magnetic induction line: E=BLv

3. When the conductor rod rotates around one end to cut the magnetic induction line: E=BL2ω

4. When the lead frame rotates around the axis perpendicular to B: E=NBSω.

Seeing these formulas, do you recall the fear of being dominated by high school physics?

cough cough

It was on this basis that Xu Yun wrote another formula that made Faraday's scalp tingle:

▽×(▽×E)=▽(▽·E)-(▽·▽)E=▽(▽·E)-▽E

▽T=T/X+T/y+T/z.

That's right.

Smart classmates must have seen it.

The first small formula is the curl of the electric field E by the triple product formula of the vector, and the second is the Laplace of the electric field.

Among them, the name of curl is curl, a vocabulary proposed by wheat in 1871.

However, related concepts appeared as early as 1839 in the construction of optical field theory, but they have not been formally summarized.

Actually.

Based on Faraday's mathematical accumulation, he probably couldn't understand this formula instantly, and needed more in-depth analytical calculations.

However, considering that some rare students who fail the exam are almost crying, it is assumed that Faraday is possessed by Gauss

After looking at the formula written by Xu Yun, Weber, who had the highest level of real mathematics among the people present, realized something again.

He frowned and stared at the formula for half a minute, and suddenly his eyes lit up.

Flatten the left hand, make a fist with the right hand, and knock heavily on the palm:

"This is the value that can be obtained by subtracting the Laplace of the electric field from the gradient of the electric field divergence?"

Xu Yun gave him a thumbs up. No wonder some people in later generations said that if Weber had not entered electromagnetism, perhaps a giant would appear in the history of mathematics.

This kind of thinking sensitivity is rare even in later generations.

in the formula above.

▽(▽·E) represents the gradient of the divergence of the electric field E, and E(▽·▽) can be replaced by (▽·▽)E, and can also be written as ▽E—this leads to the following Laplace operator.

As long as it is assumed that the temperature of a point (x, y, z) in space is represented by T (x, y, z), then this temperature function T (x, y, z) is a scalar function, and the gradient can be taken for it▽ T.

And because the gradient is a vector—the gradient has a direction, pointing to the direction with the fastest change, so we can take the divergence▽· for it.

As long as the expansion of the ▽ operator and the rule of vector coordinate multiplication are used, the divergence of the gradient of the temperature function T (x, y, z) (that is, ▽T) can be expressed.

Very simple and very easy to understand.

Well, the pure mathematical derivation ends here. (There are a lot of reductions, if there is any link that is difficult to understand, you can leave a message, and I will try my best to answer)

Then Xu Yun looked at Mai Mai again, and said:

"Student Maxwell, I will give you another task to use the Laplace operator to express the wave equation we obtained before."

Mai Mai's mood at this time has long been attracted by the formula written by Xu Yun. Hearing this, he picked up the pen almost subconsciously, and quickly calculated it.

But I don't know why.

In his heart, he always felt that this formula was inexplicably kind.

He even had a very subtle, inexplicable feeling:

When I saw Xu Yun listed this formula.

He seemed to see his girlfriend holding someone else's hand and kissing wantonly in front of him

Oh, I don't have a girlfriend, that's fine.

And the other side.

If Xu Yun could know what Mai Mai was thinking, his expression would probably be a little weird.

Because in a sense.

This is indeed the behavior of the tauren:

The formula he listed is nothing but one of the expressions of Maxwell's equations under the Laplace operator

It's a pity that Mai Mai won't ask, and Xu Yun won't say it either. I'm afraid this matter will become a mystery that no one knows.

Afterwards, Maimai took a deep breath and put all his thoughts on the simplification of the formula.

When Xu Yun was writing novels in his previous life, a reader once raised a question that was quite quality.

The one-dimensional wave equation appeared in 1746, why re-deduce the formula?

The answer is simple:

Although d'Alembert once worked out the one-dimensional wave equation, what he worked out was the initial solution of traveling waves.

This kind of solution is also called the general solution, and it is actually very, very different from the wave equation of later generations.

What Xu Yun listed this time is the general solution in 1865, so there is no bug of "the wave equation has not been derived in this world line".

Don't say anything else.

The idea of ​​Fourier change needed in the classical wave equation alone was not summarized by Fourier until 1822 and published in "The Analytical Theory of Heat".

The line of sight returns to reality.

This moment.

Mai Mai is like a passionate warrior of pure love, humming and humming while doing calculations on paper:

"Curl is taken on both sides."

"▽·E=0"

Swish Swish Swish——

With the jump of the pen tip.

The simplified data item by item appeared on the paper.

And with the appearance of these expressions, the breathing of many bigwigs on the scene gradually became heavy.

Except for William Whewell and Prince Albert, the only solver, Wheat, has not yet realized the seriousness of the problem.

After all, he is still just a student in the Department of Mathematics. He has not yet been formally exposed to electromagnetism, and he does not have enough physical sensitivity.

He just simplified and calculated the formula at the mathematical level, and he didn't have enough brainpower to think about the issue of 'meaning'.

However, as the calculation came to the final stage, when the answer was about to be written down, no matter how slow people were, it was time for them to react.

I saw this Scottish young man counting, and the tip of his pen stopped suddenly.

He raised his head in surprise and looked at Xu Yun, his face flushed a little:

"Mr. Luo Feng, doesn't this formula just explain it?"

Xu Yun nodded slightly towards him, sighed secretly, and said:

"That's right, finish writing it, it's time to unseal certain things."

Gollum—

Mai Gan dryly swallowed her saliva, and glanced quickly across the classroom.

Faraday, Thomson, Weber, Joule, Stokes.

This moment.

These bigwigs, who accounted for one-third of the thickness of the high school physics textbooks of later generations, stared solemnly at the tip of Mai's pen.

Weber's lips were trembling faintly, Faraday was holding a vial in his hand, and Stokes' fist was clenched quietly.

Even Joule's big bald head seems to reflect a lot of light.

They are waiting.

Wait to witness a mathematical miracle.

"call"

Mai Mai puffed her cheeks, took a deep breath, and made the final calculation on the paper.

"μ0 and ε0 are both constants, so the right side naturally becomes to calculate the partial derivative of the electric field E twice."

"Arrange the minus signs again, finally."

A few minutes later.

An expression for the final term appears on the parchment:

▽B=μ0ε0(B/t).

▽E=μ0ε0(E/t).

The former is the equation of the electric field intensity E, and the latter is the equation of the independent magnetic induction intensity B.

As the expression was written, the classroom immediately became audible.

Faraday panted heavily, took out the nitroglycerin again tremblingly, and swallowed it sublingually

Seeing a few excited bosses who looked like Parkinson's patients, William Whewell on the side couldn't help but exchanged glances with Prince Albert, and asked:

"Well, some professors, I would like to ask you, what is the meaning of this expression?"

Only then did Stokes remember that there were few people at the scene, so he turned his head and explained to William Whewell:

"Mr. Whewell, you are an authority in the field of philosophy, so there may be some... well, barriers in the professional knowledge of natural science."

As he spoke, he pointed to the classic wave equation deduced by Xu Yun earlier, and continued:

"First of all, we know that classmate Luo Feng or Mr. Fat Yu, the classic wave equation he deduced is absolutely mathematically valid."

"That is, where this mathematical formula is met, there must be waves."

Xu Yun listened to his words and did not correct Stokes' mistake - after all, everyone did not know the concept of quantum at this time.

Stokes then said:

"Then Luo Feng introduced the concepts of electric field and magnetic field. After calculation, the expressions still hold. What do you think this means?"

William Whewell was slightly taken aback, and somewhat understood what Stokes meant:

"That is, there are waves in both electromagnetism and magnetic fields?"

Faraday on the side also took a breath at this time, nodded heavily, and added:

"To be precise, it should be mathematically verified that both the electric field and the magnetic field propagate in space in the form of fluctuations, and there is a wave that has never been discovered in the field."

"never found"

Say the last.

Faraday's tone was almost murmured.

Up to now, he can now understand the meaning of Xu Yun's phrase "the seal is lifted":

In the electromagnetic field that I have studied for decades, there is an unknown wave!

Such an important thing, I didn't know anything about it before.

Seeing Faraday with an uncertain expression, Xu Yun couldn't help feeling a little emotional.

When he was in high school, he once happened to read an article.

The title of the article is "Faraday's Regret".

Of course.

This article is not chicken soup published in Readers or Yilin.

Instead, it was serialized in a short article called Learning News that was common when Xu Yun was studying.

That kind of newspaper costs more than 50 yuan a semester, and 90% of the pages are all kinds of topics, but sometimes some articles are printed in the corners.

This study newspaper and another book called "Current Affairs" were considered to be one of the few channels through which Xu Yun could get in touch with social news when he was studying.

I don't know if these things still exist after 20 years.

all in all.

In "Faraday's Regrets."

The author said that because Faraday was not well educated, his language level was very low, and his papers were obscure and difficult to understand.

Therefore, his series of major discoveries did not cause much shock at the time.

Wheat received excellent education, so he summed up electromagnetic waves.

There are a lot of articles in Barabara, and finally I wrote a summary:

[Primary and middle schools are the period for learning knowledge and laying the foundation, and you should learn all kinds of homework well. Among them, the Chinese class is a basic class and a tool class for learning all kinds of homework. It should not be underestimated, and it must not repeat Faraday’s regret].

Xu Yun didn't have any idea at the time. After all, he was only in high school at that time, so he didn't know the specific life of Faraday.

But when I went to university and studied the history of physics, I realized that this shit is nonsense, isn't it?

When Faraday was alive, he was almost confessed and worshiped. The generator he developed could become the soul of the second industrial revolution. How could anyone ignore him?

On the contrary, Mai Mai only had a bright moment while studying at Cambridge University, and her life has been unsatisfactory since then.

In addition, if we talk about obscurity, Maxwell's equations are infinitely more difficult to understand than Faraday's magnetic field lines.

Not to mention that Xu Yun later read the scanned English version of Faraday's papers, the content of which is not difficult to understand even with the cognition of the 19th century.

But on the other hand.

Although Faraday himself may not have felt it until his death, from the perspective of God in the future, electromagnetic waves can undoubtedly be said to be the greatest regret in Faraday's life.

Because of the accumulation of research in Faraday's life, he should be able to deduce electromagnetic waves.

For example, the Newman vector potential proposed by Newman in 1845, adding the magnetic field law and then finding the curl, can obtain the approximation of the magnetostatic equation.

This is actually very close to electromagnetic waves.

At the same time, in some letters left by Faraday, future generations can also find some guesses about electromagnetic waves.

For example, in a letter to Weber in 1865, Faraday wrote a sentence:

".Maybe between the electrified conductor and the conductor, there is some kind of unknown force that is transmitting and interacting in the space that we cannot see with the naked eye."

It's a pity that Faraday's mathematics has always been bad, so the person who finally predicted electromagnetic waves through derivation was Wheat, and Hertz proved it for him.

So from Xu Yun's perspective.

It is a pity that Faraday did not discover electromagnetic waves, and it is even unfair.

After all, electromagnetic waves are a concept that can be called the heart of electromagnetism.

This is like a marine biologist who has studied blue whales all his life, and has an incomparable understanding of the migration routes, calls, and living habits of blue whales.

However, due to the underdeveloped deep diving technology, he has never seen a blue whale fall in his life, and he has encountered many shark falls.

This is obviously a pity.

So although Xu Yun's mission target this time is wheat, after hesitating for a long time, he decided to lift the 'seal' on the electromagnetic waves.

This is also the root cause of his feeling of indebtedness to wheat and Hertz mentioned earlier.

after awhile.

The mentality of Faraday and others gradually returned to normal, and they began to think about other issues when they had time.

He stared at the expression derived by Mai for a few seconds, frowned slightly, and said to Xu Yun:

"Student Luo Feng, although you have proved mathematically that there are waves in electric and magnetic fields, physics and mathematics are still somewhat different."

"If a class of matter is only established mathematically, it can only be called a prediction at best."

"If you want to finally confirm its existence, then you must come up with evidence that is visible to the naked eye and so on!"

Before finishing the second half of the sentence, Faraday suddenly realized something.

I saw his eyes fixed on Xu Yun, and there was some anticipation on the old handsome face, and he asked:

"Student Luo Feng, you said earlier that you have two things to do today, one is derivation and the other is experiment."

"Could it be that the experiment refers to"

Xu Yun nodded slightly towards him, speaking slowly but surely:

"That's right, what we're going to do next is"

"Catch the waves in the electromagnetic field!"