I Just Want to Be a Quiet Top Student

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

"Well, I'm sorry." Shen Qi rubbed his temples. Recently, he was revising the manuscript of "Olympiad Champion Shen Qi's Mathematical Skills". He was mentally and mentally haggard and hadn't had a good rest.

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

After reviewing the last 25-point calculation question, Shen Qi finally became interested: "Just this last question, it seems like a regular physics teacher's question."

Most physics calculation questions are accompanied by schematic diagrams. Physics questions without pictures generally present two extremes, one is simple to doze off, and the other is difficult to hang up.

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

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

The text description of this topic is:

"As shown in the figure, a uniformly charged ring with a linear charge density of λ (λ \u003e 0) and a radius R is fixed on a smooth horizontal insulating table. A smooth ball with a mass m and an electric charge q is placed at rest on the table at a position very close to point O in the center of the ring."

"Assuming that the distribution of charge on the ring is not affected by the charge of the ball, try to judge whether the subsequent motion of the ball is vibration?"

"If it is vibration, set the distance r0\u003c\u003cR between the initial position of the ball and the point O, and use an appropriate approximation method to estimate the vibration period T of the ball."

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.

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

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

Obviously, this is a question about electromagnetism. Among many estimation methods, Shen Qi chose the Gauss theorem of electrostatic field as the basis to start answering the question.

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

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

Extend this circle along the positive and negative directions of the x-axis by l, and a cylindrical surface is formed.

Shen Qi took 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' theorem was introduced, the truth became clearer and clearer.

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

Shen Qi quickly solved the first question, which is to give conclusions qualitatively. Students who have received training in Wujing should be able to give correct conclusive judgments.

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

The electric flux on the two ends of the cylinder can be approximated by the electric field strength on 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 approximation of the electric flux through the two faces comes out:

Both ends E*ds≈E1*2πr^2

The electric flux passing through the side of the cylinder can be approximated by the electric field intensity Er at a distance r from point O on the circular plane, and 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 do simple harmonic vibration around the O point under its action.

So the period T=4πR root sign εm/λq

"It's done." After being baptized by the CMO and even the IMO, Shen Qi is already an experienced veteran in the field of academic competitions.

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

Since he is a veteran player, he cannot be arrogant, irritable and pompous, and must always maintain a rigorous competitive style.

Shen Qi checked the exam papers, and then handed in the papers. At this time, more than 30 minutes had passed since the exam started.

"This shit?"

"What the hell?"

"Submit papers so early?"

"Writing non-stop, it takes 30 minutes to fill the test paper, right?"

"You don't need to think about this guy? Or just write it blindly?"

The other contestants in the same examination room were obviously affected by Shen Qi's handing in the paper, and each shouted MMP in their hearts.

Although the examination papers for the CPhO National Preliminary Competition are not difficult, it is rare to submit the papers so early.

There are also sharp-eyed contestants in the Wujing circle: "The guy who handed in the paper early...could it be Shen Qi? The champion of the International Mathematical Olympiad?"

When Shen Qi walked to the entrance of the examination room, he sneezed suddenly, and a chill ran down his spine.

"Who is scolding me?" Shen Qi suddenly turned his head, scanning the contestants with sharp eyes.

"Grass!"

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

"Hey, please leave the examination room quickly after handing in the test paper." The invigilator urged Shen Qi, and quickly looked at Shen Qi's test paper. Everything that should be written was filled with reason and evidence. Many hours to hand in papers.

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

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

Shen Qi was a little calm: "It's average, the third in Asia."

"Then who are the top two in Asia?" Mu Rong held back from laughing.

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

"Haha." Mu Rong finally couldn't help laughing, and felt puzzled again: "With your political consciousness, you can't get a B in the political exam, right?" She also heard that Shen Qi got a B in the political exam, and the rest The doors are all A.

"Hey, who has never been young and ignorant." Shen Qi gets upset when he thinks about political exams, black history, a stain that cannot be erased. Of course, before the second semester of the second year of high school, Shen Qihei had a lot of history, since it cannot be erased, then face it calmly.

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

"Go, go home and have a good rest. You've worked hard." Mu Rong didn't discuss any issues with Shen Qi, and Shen Qi's actions explained everything.

The marking of the preliminary round will be completed within one to two weeks, and the CPhO rematch will be held in mid-April.

On the second day, Shen Qi met some teammates of the school's sports team in Nangang No. 2 Middle School.

"After I estimate the score, I think I can get 140 in the test?" said Lin Xingyu, a teammate of the Wujing team.

"I made a mistake in one multiple-choice question, two fill-in-the-blank questions, and two calculation questions, and my score in the preliminary round was between 120 and 130." Bai Lingye, another teammate, said.

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

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

"Bull!" Lin Xingyu had a kind of blind admiration for Shen Qi, 200 points is a perfect score.

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

"Bai Lingye, I'm afraid you failed in math." Lin Xingyu said, "There are so many contestants from all over the country participating, and a perfect score will raise the score line? You won't even complain, bad review!"

...

...

(Yesterday, I drank too much at a relative's house on the second day of junior high school. I just woke up and my head hurt. I got up and sent a chapter to save the manuscript and then went back to sleep. I don't think I can type a few words today. I have to go to other relatives' house for dinner at night. I will celebrate the New Year in my hometown. 20 Men over the age of 10 who do not drink alcohol are not allowed.

I received a notice from the starting point that it will be on the shelves on March 1. I have to save some manuscripts. It is estimated that it will be difficult to save a chapter today, so I can only update one chapter. )