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

"Well, I'm sorry. Shen Qi rubbed his temples, and recently changed the draft of "Mathematical Skills of Olympiad Champion Shen Qi", and he was haggard and didn't have much rest.

"Hurry up and finish the last calculation problem, and go home to catch up on sleep. Shen Qi cheered up and carefully examined the question.

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

Most of the physics calculation problems are equipped with schematic diagrams, and the physics problems without drawings generally present two extremes, one is a simple want to doze off, and the other is a difficult hanging explosion.

The preliminary round has the highest score of 25 points, and this calculation is accompanied by a schematic diagram.

The diagram is a circle, with a dashed line R drawn from the center of the circle O to the seven o'clock around the circle, and this dashed line R is the radius of the circle. There is a small black dot mq not far from the center of the circle O.

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 to a smooth, horizontally insulated tabletop. A smooth ball with a mass of m and an electric charge of q is placed on the table very close to the center O point of the ring. ”

"Let the distribution of the charge on the ring not be affected by the charge of the ball, and try to determine whether the motion of the ball after it is vibration?"

"If it is vibration, let the distance r0<

The difference between estimation and rigorous calculation is that estimation can bypass complex mathematical calculations and directly obtain correct qualitative conclusions and relatively close coarse quantitative results.

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

For the same physics problem, if the estimation method is used, there is often more than one way to choose.

Obviously, this is an electromagnetism question, and Shen Qi chose Gauss's theorem of electrostatic field as the basis for answering the question among many estimation methods.

Shen Qi made an auxiliary diagram and took the axis perpendicular to the plane of the torus through the O point as the x-axis.

On the plane of the circle, take the point O as the center of the circle, and make a circle with radius r.

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

Shen Qi takes this cylindrical surface as a Gaussian surface, because there is no charge in it, according to Gauss's theorem:

∯E*ds=0

As soon as Gauss's theorem was revealed, the truth became clearer and clearer.

The electrostatic force of the positively charged ball is always directed towards the center of the ring O point, which is a restorative conservative force, and the motion of the ball is vibration, and the center of vibration is the O point.

Shen Qi quickly solved the first question, which is to give a qualitative conclusion, and students who have received training in physical competition should be able to give a correct conclusive judgment.

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

The electric flux at both ends of the cylinder can be approximated by the electric field strength on the x-axis, and Shen Qi calculates:

E1=λ（2πR）l/4πε（R^2+l^2）^3/2=λRl/2ε（R^2+l^2）^3/2

Then the approximation of the flux through the two ends comes out:

∫∫ both ends of E*ds≈E1*2πr^2

The electric flux on the side of the cylinder can be approximated by the electric field strength Er at a distance of r from the point O on the circular plane, according to Gauss's theorem:

∮∮ cylindrical surface E*ds=∫∫ both ends E*ds+∫∫ side E*ds=0

Then the electrostatic force on the charged ball at r is:

Fr=qEr=-λq/4εR^2*r

Considering the linear restoring force, the ball will vibrate in simple harmonic motion around the O point under its action.

So the period T=4πR, the root number εm/λq

"That's it. "After the baptism of CMO and even IMO, Shen Qi is already an experienced veteran in the field of discipline competitions.

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

Since he is a veteran, he must not be arrogant, irritable and exaggerated, and must always maintain a rigorous competition style.

Shen Qi checked the exam papers, and then handed in them, more than 30 minutes had passed since the start of the exam.

"This Nima?"

"?"

"Submit the paper so early?"

"If you keep writing, it will take you 30 minutes to fill the test paper, right?"

"Don't you have to think about this? Or do you write a few things blindly?"

The other players in the same examination room were obviously affected by Shen Qi's handing in the papers, and they each chanted MMP in their hearts.

Although the CPhO National Preliminary Exam is not difficult, it is rare to submit the papers so early.

There are also sharp-eyed players in the competition circle: "Submit this product in advance...... Could it be Shen Qi, the champion of the International Mathematics Olympiad?"

Shen Qi walked to the door of the examination room, sneezed, and suddenly sneezed, and a chill appeared in his spine.

"Who is scolding me?" Shen Qi turned his head suddenly, his eyes sharpened and glanced at the players.

"Grass!"

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

"Hey, please leave the exam room quickly after handing in your papers. The invigilator urged Shen Qi and quickly examined Shen Qi's test papers, which should have been written full, reasonable, not like blindness, this situation allows more than two hours in advance to hand in the papers.

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

"This ...... Shen Qi, you're too fast, aren't you?" Mu Rong was a little surprised.

Shen Qi was a little calm: "General, third in Asia." ”

"Who are the top two in Asia?" Mu Rong couldn't help but let 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 are politically conscious, it is impossible to get a B in the political exam, right?" She also heard that Shen Qi took a B in the political exam, and the rest of the subjects were A.

"Hey, who hasn't been young and ignorant. "Shen Qi is unhappy when he thinks of political exams, black history, a stain that can't be erased. Of course, before the second semester of the second semester of high school, Shen Qihei had a lot of history, and since he couldn't erase it, he would face it calmly.

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

"Go ahead, go home and have a good rest, it's hard work. Mu Rong didn't discuss any issues with Shen Qi, and Shen Qi's actions said it all.

The preliminary round will be completed in one to two weeks, and the CPhO semi-final will be held in mid-April.

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

"After I finished estimating the score, do you think I can get a 140?" said Lin Xingyu, a teammate of the competition team.

"I got one multiple-choice question, two fill-in-the-blank questions, and two calculation questions wrong, and my score in the preliminary round was probably between 120 and 130. Another teammate, Bai Lingye, said.

"What about you, Big Guy Shen Qi?" Lin Xingyu asked.

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

"Cow!" Lin Xingyu has a kind of blind worship for Shen Qi, 200 points is a full score.

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

"Bai Lingye, I'm afraid you're failing math. Lin Xingyu said, "There are so many contestants across the country participating in the competition, and a full score will raise the score line?

......

......

(Yesterday, the second day of junior high school drank too much at a relative's house, just got up, my brain hurts, I get up and send a chapter to save the manuscript and then go to sleep, today I don't estimate a few words, I have to go to other relatives' houses for dinner at night, in my hometown for the New Year, men over 20 years old are not allowed to drink.)

I received a notice from the starting point.,On the shelves on March 1st.,I have to save some drafts.,It's estimated that it's difficult to save a chapter draft today.,So I can only update one chapter.。 ）