Into Unscientific

  Chapter 259 Witness a miracle! (middle)

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

   Long ago, people discovered that there are forces between charges and between magnets.

   But initially, the two effects were not linked.

  Until people discovered that some stones struck by lightning were magnetic, they speculated 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 mentioned earlier.

  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 just to commemorate Faraday's contribution, so 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, so I won’t explain them 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.

   Exactly.

  Smart classmates must have seen it.

  The first small formula is the curl of the curl of the electric field E derived from 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, which was a vocabulary proposed by wheat in 1871.

  But 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 in an instant, and needed more in-depth analytical calculations.

  However, considering that some rare students who fail the subject are about to cry, here it is assumed that Faraday is possessed by Gauss

   Then 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.

  Straighten your left hand, make a fist with your 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 hadn't 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 above formula.

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

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.

  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 rules 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 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 Laplacian operator to represent the wave equation we obtained before."

  At this time, Xiaomai's mood has long been attracted by the formula written by Xu Yun. Hearing this, he almost subconsciously picked up the pen and started to calculate quickly.

  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, so it’s okay.

   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.

  Myself, 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 either. I'm afraid this matter will become a mystery that no one knows.

   Then Xiaomai took a deep breath and put all his thoughts on the simplification of the formula.

  In the previous life, when Xu Yun was writing a novel, a reader once raised a question that was quite quality.

  The one-dimensional wave equation appeared in 1746. Why do we need to re-deduce the formula?

   The answer is simple:

  Although d'Alembert once studied the one-dimensional wave equation, what he studied 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.

  Just the idea of ​​Fourier change that needs to be used in the classical wave equation, it was not published in "Analytic Theory of Heat" by Fourier until 1822.

  The line of sight returns to reality.

   Right now.

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

   "Take curl on both sides."

  “▽・E=0”

   Swish Swish Swish—

   With the jump of the pen tip.

  The simplified data item by item appears on the paper.

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

  In addition to William Whewell and Prince Albert, the only problem 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 comes to the final stage, when the answer is about to be written down, no matter how slow people are, they should react.

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

   Raised his head in surprise, looked at Xu Yun, his face flushed a little:

   "Mr. Luo Feng, this... This formula does not explain it"

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

   "That's right, let's finish writing it, and it's time to unseal some things."

   Gollum—

  Wheat swallowed dryly, and glanced quickly across the classroom.

   Faraday, Thomson, Weber, Joule, Stokes.

   Right now.

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

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

  Even Joule’s big bald head seemed to refract a lot of light.

   They are waiting.

   Wait to witness a mathematical miracle.

   "call"

  Mai Mai puffed his 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 the partial derivative of the electric field E twice."

   "Arrange the negative signs again, finally."

After a few minutes.

   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, and once again tremblingly took out the nitroglycerin, swallowed it sublingually

  Looking at 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, does this expression have any meaning?"

  Stokes remembered 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 established mathematically."

   "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 didn’t know the concept of quantum at this time.

  At this point Stokes said again:

   "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 to say, 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 verified mathematically 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 Discovered"

   Said the last.

  Faraday's tone was almost murmured.

   Now, he can understand what Xu Yun meant by "the seal is lifted":

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

  I didn't know anything about such an important thing before.

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

  When he was in high school, he once read an article by chance.

  The name of the article is called "Faraday's Regret".

Of course.

  This article is not chicken soup published on 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 whether 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 the papers he wrote were obscure.

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

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

  I wrote a lot of articles, and finally wrote a summary:

  【Primary and middle school is the period of 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 after studying the history of physics in college, I realized that this **** is nonsense?

   Faraday was almost confessed to when he was alive. The generator he researched 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, later generations can also find some guesses about electromagnetic waves.

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

  “.Maybe between the electrified conductor and the conductor, in the space invisible to our naked eyes, there is some kind of unknown force that is transmitting and interacting.”

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

   So from Xu Yun's perspective.

   Faraday did not discover electromagnetic waves, which is actually a pity, 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. He has a very good understanding of the migration routes, calls, and living habits of blue whales.

  However, because of 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.

   Faraday and the others gradually returned to normal mentality, and 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 verified 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 the evidence 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, the next thing we're going to do is"

   "Catch the waves in the electromagnetic field!"

  (end of this chapter)