"Student, please stay awake and don't doze off during the exam," the invigilator reminded Shen Qi sternly.
"Um, sorry." Shen Qi rubbed his temples. He had been working on revising the manuscript of "<Olympic Math Champion Shen Qi's Math Techniques>" for some time now, and it had taken a toll on his mental and physical health. He hadn't had much rest.
"Hurry up and finish the last calculation problem, then go home and catch up on some sleep." Shen Qi perked up and carefully reviewed the question.
After reviewing the last 25-point calculation problem, Shen Qi finally showed some interest. "This last problem seems like it was set by a proper physics teacher."
Most physics calculation problems are accompanied by diagrams. Physics problems without diagrams generally fall into two extremes: one is so simple that it makes you want to doze off, and the other is so difficult that it's insane.
The preliminary round's "treasure trove" question had the highest score, 25 points, and this calculation was accompanied by a diagram.
The diagram shows a circle with a dashed line R drawn from the center O to the 7 o'clock position on the circumference. This dashed line R is the radius of the circle. There is a small black dot mq not far from the center O.
The textual description of this question is:
"As shown in the figure, a uniformly charged circular ring with linear charge density λ (λ>0) and radius R is fixed on a smooth, horizontal, insulated table. A smooth ball with mass m and charge q is at rest on the table, very close to the center point O of the circular ring."
"Assuming the charge distribution on the ring is unaffected by the charge on the small ball, determine whether the subsequent motion of the small ball is an oscillation?"
"If it is an oscillation, assuming the initial distance between the ball and point O is r0 << R, try to estimate the oscillation period T of the ball using an appropriate approximation method."
The difference between estimation and rigorous calculation is that estimation can bypass complex mathematical calculations and directly obtain correct qualitative conclusions and relatively close rough quantitative results.
Regarding the final calculation problem in the preliminary round, Shen Qi had to provide a qualitative conclusion on whether the ball's motion was oscillating or non-oscillating, and the judgment had to be accurate. This was the first step.
For the same physics problem, if estimation is used, there is often more than one approach to choose from.
Clearly, this was an electromagnetism problem. Among various estimation methods, Shen Qi chose Gauss's Theorem electrostatics as the basis for his answer.
Shen Qi created an auxiliary diagram, taking the axis passing through point O and perpendicular to the annular plane as the x-axis.
Draw a circle with center O and radius r on the circular plane.
Extend this circle by 1 in both the positive and negative x-axis directions to form a cylindrical surface.
Shen Qi chose this cylindrical surface as the Gauss surface because it contains no electric charge. According to Gauss's Theorem, we can obtain:
E*ds=0
With Gauss's Theorem in hand, the truth becomes increasingly clear.
The electrostatic force on the positively charged ball always points towards the center O of the ring. It is a restoring conservative force, and the ball's motion is an oscillation, with the center of the oscillation being point O.
Shen Qi quickly solved the first question, which is to give a qualitative conclusion. Students who have received physics competition training should be able to give the correct conclusive judgment.
The second question requires Shen Qi to estimate the oscillation period T of the small ball, which is a little more complicated.
The electric flux through the two ends of a cylinder can be approximately calculated using the electric field strength along the x-axis. Shen Qi made the calculation:
E1=λ(2πR)l/4πε(R^2+l^2)^3/2=λRl/2ε(R^2+l^2)^3/2
Then the approximate values of the electric flux through the two ends can be obtained:
E*ds≈E1*2πr^2 for both ends
The electric flux through the side of the cylinder can be approximately calculated using the electric field intensity Er at a distance r from point O on the circular plane, according to Gauss's Theorem:
Cylindrical surface E*ds = End face E*ds + Lateral face E*ds = 0
The electrostatic force on the charged ball at point r is:
Fr=qEr=-λq/4εR^2*r
Considering the linear restoring force, the ball will undergo simple harmonic motion around point O under its influence.
Therefore, the period T = 4πR√εm/λq
"Done." Having experienced the CMO and even the IMO, Shen Qi is already considered a veteran in the field of academic competitions.
Whether it's math competitions or physical competitions, the competition formats are largely the same.
As a veteran, one cannot be arrogant, conceited, or irritable; one must always maintain a rigorous competitive spirit.
Shen Qi checked the exam paper once and then handed it in. At this point, more than 30 minutes had passed since the start of the exam.
"What the hell?"
"Holy crap?"
"Handing in the paper so early?"
"If you keep writing, it will take at least 30 minutes to fill the entire test paper, right?"
"Does this guy not need to think? Or is he just writing whatever comes to mind?"
The other test takers in the same exam room were clearly affected by Shen Qi handing in his paper, each inwardly cursing "MMP" (a vulgar expression of frustration).
Although the CPhO national preliminary exam was not difficult, it is still rare to submit the paper so early.
Among the physics competition circle, some sharp-eyed contestants remarked, "This guy who handed in his paper early... could it be Shen Qi? That International Mathematical Olympiad champion?"
Shen Qi walked to the entrance of the examination hall, and suddenly sneezed, a chill running down his spine.
"Who's insulting me?" Shen Qi suddenly turned around, his sharp eyes scanning the contestants.
"Grass!"
The contestants' anuses trembled, so they buried their heads and continued answering questions.
"Hey, please leave the exam room quickly after you hand in your paper." The invigilator urged Shen Qi and quickly reviewed Shen Qi's exam paper. It was full of writing, logical and well-reasoned, not just guesswork. In this case, it was allowed to hand in the paper more than two hours early.
Shen Qi strode away and met Mu Rong outside the examination hall.
"This... Shen Qi, you're too fast!" Mu Rong, somewhat surprised.
Shen Qi replied calmly, "So-so, third in Asia."
"Then who are the top two in Asia?" Mu Rong tried to suppress her laughter.
Shen Qi said in a serious tone, "It's the principal Teacher Mu."
"Haha." Mu Rong finally couldn't help but laugh, then wondered, "With your political awareness, it's impossible for you to get a B in the political exam, right?" She had also heard that Shen Qi got a B in the political exam, but A in the other subjects.
"Sigh, who hasn't been young and naive?" Shen Qi felt annoyed whenever he thought about the political exam; it was a dark history, an indelible stain. Of course, Shen Qi had quite a few dark histories before the second semester of his junior year, and since he couldn't erase them, he would face them with equanimity.
Shen Qi stretched. "Yawn... I'm so sleepy, I'm going to sleep."
"Go on, go home and get some rest. You've worked hard." Mu Rong didn't discuss any issues with Shen Qi; Shen Qi's actions spoke for themselves.
The preliminary round marking will be completed within one to two weeks, and the CPhO semi-finals are scheduled for mid-April.
The next day, Shen Qi met several teammates from the school's Physics Competition Team at Nangang Second High School.
"After estimating my score, I think I can get 140?" said Lin Xingyu, a teammate on the Physics Competition Team.
"I got one multiple-choice question, two fill-in-the-blank questions, and two calculation questions wrong. My score in the preliminary round was probably between 120 and 130," said another teammate Bai Lingye.
"And you, Boss Shen Qi?" Lin Xingyu asked.
"I estimate around 200 points? Maybe I'll lose a point or two on some steps in the last calculation problem, who knows?" Shen Qi said.
"Awesome!" Lin Xingyu had a blind admiration for Shen Qi; 200 points was a perfect score.
"It's over, it's over! Shen Qi has raised the cutoff score for the preliminary rounds," Bai Lingye said bitterly.
"Bai Lingye, you probably failed math," Lin Xingyu said. "With so many contestants nationwide, one perfect score raises the passing score? You don't even know how to criticize properly, thumbs down!"
(I got drunk at a relative's house yesterday, the second day of the Lunar New Year. I just woke up with a headache. I'll post a chapter from my draft and then go back to sleep. I probably won't be able to write much today. I'm going to eat at another relative's house tonight. In my hometown, men over 20 are not allowed to not drink alcohol during the Lunar New Year.)
I received a notification from Qidian that the book will be available for purchase on March 1st. I need to save up some drafts, but I probably won't even be able to save up one chapter today, so I can only update one chapter.