"Student, please stay awake and don't doze off in the examination room." The invigilator reminded Shen Qi very seriously.

"Yeah, sorry." Shen Qi rubbed his temples and recently changed the manuscript of "Mathematical Skills of Mathematical Olympiad Shen Qi" to make him exhausted and didn't have much rest.

"Hurry up the last calculation question, go home to make up for your sleep after finishing it." Shen Qi cheered up and carefully reviewed the question.

After reviewing the last 25-point calculation question, Shen Qi finally became a little interested: "This last question is like a question given by a regular physics teacher."

Most physics calculation questions are equipped with schematic diagrams. Physics questions that do not include pictures generally show two extremes. One is to simply want to doze off, and the other is to be difficult to make a fuss.

The score for the first-time home-selling question is the highest, with 25 points, and this calculation is equipped with a schematic diagram.

The schematic diagram is a circle, with a dotted line r drawn from the center o of the circle to the seven o'clock position of the circle. This dotted line r is the radius of the circle. There is a small black dot mq not far from the center o of the circle.

The text description of this question is:

"As shown in the figure, a uniform dotted ring with a charge line density of λ (λ>0) and a radius of r is fixed on a smooth horizontally insulated desktop. A smooth ball with a mass of m and a charge of q is placed still on the table at a position very close to the center of the ring."

"Suppose the distribution of charge on the ring is not affected by the charge of the small ball, try to judge whether the movement of the small ball afterwards is vibration?"

"If it is vibration, let the distance r0 of the initial position of the ball and point o is 0 <
The difference between estimation and strict calculations is that estimation can bypass complex mathematical calculations and directly obtain correct qualitative conclusions and relatively close rough quantitative results.

As for the last calculation question of the preliminary round, Shen Qi must give a qualitative conclusion to whether the movement of the ball is vibrating or not vibrating, and the judgment must not be wrong. This is the first step.

For the same physics problem, if an estimation method is used, there are often more than one option.

It is obvious that this is a question about electromagnetics. Among the various estimation methods, Shen Qi chose the electrostatic field Gaussian theorem as the basis to start answering the questions.

Shen Qi made an auxiliary diagram, taking the axis passing through the o-point and perpendicular to the plane of the ring as the x-axis.

On the plane of the circle, point o is the center and make a circle with a radius r.

The circle is extended l in the positive and negative directions of the x-axis, and a cylindrical surface is formed.

Shen Qi took this cylindrical surface as the Gaussian surface, because there was no charge in it, according to the Gaussian theorem, you can obtain:

?e*ds=0

Once Gauss' theorem was put out, the truth became clearer and clearer.

The electrostatic force received by a positively charged ball always points to the o-point in the center of the ring, which is a restorative conservative force. The movement of the ball is vibration, and the center of the vibration is point o-point.

Shen Qi quickly solved the first question, which is to give a qualitative conclusion. Students who have received training in the field of competition should be able to give correct concluding judgments.

The second question asked Shen Qi to estimate the vibration period t of the ball, which was a little troublesome.

The electrical fluxes on both end surfaces of the cylinder can be calculated approximately using the electric field intensity on the x-axis, and Shen Qi made the calculation:

e1=λ(2πr)l/4πe(r^2+l^2)^3/2=λrl/2e(r^2+l^2)^3/2

Then the approximate value of the electrical flux through both end faces comes out:

?The two end faces e*ds≈e1*2πr^2

The electric flux on the side of the cylinder can be calculated approximately using the electric field intensity er at the distance between o and point o on the circular plane. According to Gaussian theorem, we can obtain:

?Cylindrical surface e*ds=?Two end surfaces e*ds+?Side surfaces e*ds=0

Then the charged ball receives static electricity at the r location:

fr=qer=-λq/4er^2*r

Considering the linear restoration force, the ball will perform simple harmonic vibrations around the o-point under its action.

Therefore, the period t=4πr root number em/λq

"Do it." After the baptism of CMO and even IMO, Shen Qi has become an experienced veteran in the field of subject competitions.

Whether it is digital competition or competition, the competition mode is similar.

Since you are a veteran, you cannot be arrogant, irritable and exaggerated, and you must always maintain a rigorous competition style.

Shen Qi checked the test papers and handed over the papers. At this time, more than 30 minutes had passed since the exam began.

"Damn it?"

"Damn?"

"Submit the papers so early?"

"It takes 30 minutes to write the test papers all over again, right?"

"I don't need to think about this guy? Or do I just write a few tricks?"

Other contestants in the same exam room were obviously influenced by Shen Qi's paper handing over, and each shouted MMP in his heart.

Although the test papers for the Cpho National Preliminary Competition are not difficult, it is rare to hand in the paper so early.

There are also sharp-eyed players in the competition circle: "Is this guy handing in advance... Could it be Shen Qi? The champion of the International Mathematical Olympiad?"

Shen Qi walked to the entrance of the examination room, and Ah sneezes suddenly, and a hint of chill appeared on his spine.

"Who is scolding me?" Shen Qi suddenly turned around and glanced at the contestants with sharp eyes.

"Grass!"

The contestants were shaking, so they buried their heads and continued to answer the questions.

"Hey, please leave the examination room quickly after handing in the paper." The invigilator urged Shen Qi and quickly examined Shen Qi's test paper. Everything that should be written was full, with reasonable and well-founded, unlike blindly. In this case, you are allowed to hand in the paper more than two hours in advance.

Shen Qi strode away and met Mu Rong outside the examination room.

"This... Shen Qi, you are too fast, right?" Mu Rong was a little surprised.

Shen Qi was a little calm: "Overall, the third in Asia."

"Who is the top two in Asia?" Mu Rong resisted not letting herself laugh.

Shen Qi said seriously: "It's the principal and Teacher Mu."

"Haha." Mu Rong finally couldn't help laughing, and felt puzzled again: "You have political awareness, it's impossible to get a B in the political exam, right?" She also heard that Shen Qi got a B in the political exam, and the rest were all A.

"Hey, who has never been young and has been ignorant?" Shen Qi was unhappy when he thought of the political exam. It was so dark history that it was impossible to erase. Of course, Shen Qi had a lot of dark history before the second semester of his second year of high school. Since he could not be erased, he would face it calmly.

Shen Qi stretched: "Yao... so sleepy, I'm going to sleep."

"Go, go home and have a good rest. Thank you for your hard work." Mu Rong did not discuss any of the issues with Shen Qi, and Shen Qi's actions explained everything.

The preliminary round marking work will be completed within one to two weeks, and the Cpho's rematch will be held in mid-April.

The next day, Shen Qi met several teammates from the school's football team at Nangang No. 2 Middle School.

"I've estimated the score and think I can get 140?" said Lin Xingyu, a teammate of the Football Team.

"I made a mistake in a multiple-choice question, two fill-in-the-blank questions, two calculation questions, and the preliminary score is about 120 to 130," said another teammate Bai Lingye.

"Where are you, Mr. Shen Qi?" Lin Xingyu asked.

"I guess it's around 200 points? Maybe one or two points will be deducted in some steps of the last calculation question, and I can't say it, I don't know." Shen Qi said.

"Awesome!" Lin Xingyu had a blind admiration for Shen Qi, and 200 points were the full score.

"It's over, the score line for the preliminary round of promotion was raised by Shen Qi." Bai Lingye said bitterly.

"Bai Lingye, you may not pass the math level." Lin Xingyu said, "So many contestants across the country participate in the competition, and the score line will be raised with a full score? You won't even complain, bad reviews!"

...

...

(I got drunk at my relative's house on the second day of the New Year yesterday. I just got up and my head hurts. I got up and posted a chapter to save the manuscript and then went to bed. I guess I couldn't code a few words today. I had to go to other relatives' houses for dinner at night. I spent the New Year in my hometown. It is not allowed for men over 20 to drink without drinking.

I received a notice from Qidian that it will be released on March 1, so I have to save some manuscripts. It is estimated that it will be difficult to save one chapter today, so I can only update one chapter.)
Chapter completed!