I Just Want to Be a Quiet Top Student

Chapter 87 Estimation of Gauss’s theorem

“This classmate, please stay awake and don’t doze off in the examination room.” The invigilator reminded Shen Qi very seriously.

“Um, sorry.” Shen Qi rubbed his temples. Recently, he changed the draft of “Mathematics Skills of Olympian Mathematical Champion Shen Qi”. The change made him feel tired and didn’t have much rest.

“Hurry up and finish the last calculation problem, and go home to make up for sleep after finishing it.” Shen Qi cheered up and reviewed the problem carefully.

After reviewing the last 25-point calculation question, Shen Qi finally got some interest: “This last question is like a question from a regular physics teacher.”

Physics calculation problems are mostly equipped with schematic diagrams. Physics problems without diagrams generally present two extremes. One is simple to doze off, and the other is difficult.

The first test of the town house question has the highest score, 25 points. This calculation is equipped with a schematic diagram.

The schematic diagram of 　　 is a circle. A dotted line R is drawn from the center O to the 7 o’clock position of the circumference. 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 question is:

“As shown in the figure, the linear charge density is λ (λ>0), and a uniformly charged ring with a radius of R is fixed on a smooth horizontal insulated tabletop. A smooth ball with a mass of m and an electric quantity of q is statically placed on the tabletop The upper part is very close to point O in the center of the ring.”

“Assuming that the charge distribution on the ring is not affected by the charge of the small ball, try to determine whether the movement after the small ball is vibration?”

“If it is vibration, set the distance between the initial position of the ball and point O r0<

The difference between estimation and strict calculation is that estimation can bypass complicated mathematical calculations and directly obtain correct qualitative conclusions and relatively close rough quantitative results.

As far as the final calculation question of the preliminary round is concerned, whether the movement of the ball is vibration or non-vibration, 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 an estimation method is used, there are often more than one way to choose.

Obviously, this is an electromagnetism problem. Shen Qi chose the Gauss theorem of electrostatic field as the basis for answering the problem in many kinds of estimation methods.

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

Make a circle with radius r on the plane of the circle with point O as the center.

Extend the circle along the positive and negative directions of the x-axis by l, 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 the Gauss theorem, we can get:

? E*ds=0

As soon as Gauss theorem came out, the truth became clearer and clearer.

The electrostatic force of the positively charged ball always points to the O point at the center of the ring. In order to restore the conservative force, the motion of the ball is vibration, and the center of vibration is O point.

Shen Qi quickly solved the first question. This is a qualitative conclusion. Students who have received training in physical competition should be able to give correct conclusive judgments.

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

The electric flux at both ends of the cylinder can be calculated approximately by the electric field intensity on the x-axis. Shen Qi makes the calculation:

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

Then the approximate value of the electric flux passing through the two ends comes out:

? Both ends E*ds≈E1*2πr^2

The electric flux passing through the side of the cylinder can be calculated approximately with the electric field intensity Er at a distance of r from point O on the circular plane. According to Gauss's theorem, we can get:

? Cylindrical surface E*ds=? Both ends E*ds+? Side surface 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 small ball will make a simple harmonic motion around point O under its action.

So the period T=4πR radical εm/λq

"Get it done." After the baptism of CMO and even IMO, Shen Qi has been regarded as an experienced veteran in the subject competition.

Whether it is number competition or material competition, the competition mode is similar.

Since he is a veteran, he cannot be arrogant, violent, and must maintain a rigorous competitive style at all times.

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

"This Nima?"

"Fuck?"

"Hand in paper so early?"

"Keep writing, it takes 30 minutes to fill the test paper, right?"

"I don't need to think about this stuff? Or do I write it a little bit?"

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

Although the CPhO national preliminary examination papers are not difficult, it is rare to hand in papers so early.

There are also sharp-eyed players in the sports competition circle: "This product is handed in early…could it be Shen Qi? The champion of the International Olympiad?"

Shen Qi walked to the entrance of the examination room, Ah Hee, and suddenly sneezed, causing a chill in his spine.

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

"Grass!"

All the contestants trembled and continued to answer the questions.

"Hey, please leave the examination room as soon as you hand in the paper." The invigilator urged Shen Qi, and quickly reviewed Shen Qi's test paper. It was filled with everything that should be written, and it was justified and well-founded. Unlike a blind man, this situation allows two advances in advance. Hand in paper in multiple hours

Shen Qi strode away and saw 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: "Generally average, third in Asia."

"Who is the top two in Asia?" Mu Rong resisted laughing.

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

"Haha." Mu Rong finally couldn't help but laugh, and felt puzzled: "You are politically conscious, it is impossible to get a B in the political exam?" 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 before, ignorant." Shen Qi was upset when he thought of political exams, the dark history, the stain that cannot be erased. Of course, before the second semester of high school, Shen Qihei had a lot of history Since it can't be erased, then he can face it calmly.

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

"Go, go home and take a good rest. It's hard work." Mu Rong didn't discuss any questions with Shen Qi. Shen Qi's actions explained everything.

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

The next day, Shen Qi met several teammates from the school sports team in Nangang No. 2 Middle School.

"I have finished evaluating the score, think I can get a 140?" said Lin Xingyu, a teammate of the Wujing team.

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

"How about you, Mr. 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 question. I'm not sure, I don't know." Shen Qi said.

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

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

"Bai Lingye, you might fail in math." Lin Xingyu said, "With so many contestants across the country, one full score will raise the score line? No complaints, bad reviews!"

……

……

(Yesterday, on the second day of the second day of the day, I had a big drink at my relative’s house. I just got up and my brain hurts. I woke up and sent a chapter to save and then went to bed. Men over the age of not allowed to drink alcohol.

I was notified of the starting point. It will be released on March 1st. I have to save some manuscripts. It is estimated that it will be difficult to save one chapter of the manuscript today, so I can only update one chapter. )

The difference between estimation and strict calculation is that estimation can bypass complicated mathematical calculations and directly obtain correct qualitative conclusions and relatively close rough quantitative results.

As far as the final calculation question of the preliminary round is concerned, whether the movement of the ball is vibration or non-vibration, 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 an estimation method is used, there are often more than one way to choose.

Obviously, this is an electromagnetism problem. Shen Qi chose the Gauss theorem of electrostatic field as the basis for answering the problem in many kinds of estimation methods.

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

Make a circle with radius r on the plane of the circle with point O as the center.

Extend the circle along the positive and negative directions of the x-axis by l, 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 the Gauss theorem, we can get:

? E*ds=0

As soon as Gauss theorem came out, the truth became clearer and clearer.

The electrostatic force of the positively charged ball always points to the O point at the center of the ring. In order to restore the conservative force, the motion of the ball is vibration, and the center of vibration is O point.

Shen Qi quickly solved the first question. This is a qualitative conclusion. Students who have received training in physical competition should be able to give correct conclusive judgments.

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

The electric flux at both ends of the cylinder can be calculated approximately by the electric field intensity on the x-axis. Shen Qi makes the calculation:

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

Then the approximate value of the electric flux passing through the two ends comes out:

? Both ends E*ds≈E1*2πr^2

The electric flux passing through the side of the cylinder can be calculated approximately with the electric field intensity Er at a distance of r from point O on the circular plane. According to Gauss's theorem, we can get:

? Cylindrical surface E*ds=? Both ends E*ds+? Side surface 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 small ball will make a simple harmonic motion around point O under its action.

So the period T=4πR radical εm/λq

"Get it done." After the baptism of CMO and even IMO, Shen Qi has been regarded as an experienced veteran in the subject competition.

Whether it is number competition or material competition, the competition mode is similar.

Since he is a veteran, he cannot be arrogant, violent, and must maintain a rigorous competitive style at all times.

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

"This Nima?"

"Fuck?"

"Hand in paper so early?"

"Keep writing, it takes 30 minutes to fill the test paper, right?"

"I don't need to think about this stuff? Or do I write it a little bit?"

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

Although the CPhO national preliminary examination papers are not difficult, it is rare to hand in papers so early.

There are also sharp-eyed players in the sports competition circle: "This product is handed in early…could it be Shen Qi? The champion of the International Olympiad?"

Shen Qi walked to the entrance of the examination room, Ah Hee, and suddenly sneezed, causing a chill in his spine.

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

"Grass!"

All the contestants trembled and continued to answer the questions.

"Hey, please leave the examination room as soon as you hand in the paper." The invigilator urged Shen Qi, and quickly reviewed Shen Qi's test paper. It was filled with everything that should be written, and it was justified and well-founded. Unlike a blind man, this situation allows two advances in advance. Hand in paper in multiple hours

Shen Qi strode away and saw 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: "Generally average, third in Asia."

"Who is the top two in Asia?" Mu Rong resisted laughing.

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

"Haha." Mu Rong finally couldn't help but laugh, and felt puzzled: "You are politically conscious, it is impossible to get a B in the political exam?" 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 before, ignorant." Shen Qi was upset when he thought of political exams, the dark history, the stain that cannot be erased. Of course, before the second semester of high school, Shen Qihei had a lot of history Since it can't be erased, then he can face it calmly.

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

"Go, go home and take a good rest. It's hard work." Mu Rong didn't discuss any questions with Shen Qi. Shen Qi's actions explained everything.

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

The next day, Shen Qi met several teammates from the school sports team in Nangang No. 2 Middle School.

"I have finished evaluating the score, think I can get a 140?" said Lin Xingyu, a teammate of the Wujing team.

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

"How about you, Mr. 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 question. I'm not sure, I don't know." Shen Qi said.

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

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

"Bai Lingye, you might fail in math." Lin Xingyu said, "With so many contestants across the country, one full score will raise the score line? No complaints, bad reviews!"

……

……

(Yesterday, on the second day of the second day of the day, I had a big drink at my relative’s house. I just got up and my brain hurts. I woke up and sent a chapter to save and then went to bed. Men over the age of not allowed to drink alcohol.

I was notified of the starting point. It will be released on March 1st. I have to save some manuscripts. It is estimated that it will be difficult to save one chapter of the manuscript today, so I can only update one chapter. )