问题 计算题

(2012年2月天水一中检测)如图所示,圆形区域的匀强磁场,磁感应强度为B、方向垂直纸面向里,边界跟y轴相切于坐标原点O O点处有一放射源,沿纸面向各方向射出速率均为v的某种带电粒子,带电粒子在磁场中做圆周运动的半径是圆形磁场区域半径的两倍。已知该带电粒子的质量为m、电量为q,不考虑带电粒子的重力。

(1)推导粒子在磁场空间做圆周运动的轨道半径;

(2)求粒子通过磁场空间的最大偏转角;

(3)若粒子与磁场边界碰撞后以原速率反弹,则从O点沿x轴正方向射入磁场的粒子第一次回到O点经历的时间是多长?(已知arctan2=

答案

(1)(2)(3)

(1)带电粒子进入磁场后,受洛仑兹力作用,由牛顿第二定律得:

, 

(2)设粒子飞出和进入磁场的速度方向夹角为φ

x是粒子在磁场内轨迹的两端点的直线距离。

x最大值为2R对应的就是φ最大值.,由题述2R=r

所以

(3)设粒子与边界相邻两次碰撞过程通过的弧长所对的圆心角为2θ,该弧长所对磁场边界圆的圆心角为2β。如图所示。

则tan=,      =

由图中的几何关系,可得θ+β=π/2,=

要使粒子还能通过O点,应满足

均为正整数)

均为正整数)

当粒子第一次回到O点,应取

又α粒子在磁场中做匀速圆周运动的周期

所以从O点沿x轴正方向射出的粒子第一次回到O点经历的时间是

阅读理解

阅读理解。

      A man went to a fast-food restaurant to buy his lunch.

     "Hi,"a waiter said. "May I help you?"

     "I'd like a hamburger, large chips and a Coke,"the man said.

     "Is that for here or to go?"the waiter asked.

     "To go," the man said.

     The waiter put the man's lunch in a bag. The man took out his money and paid for his lunch.

     "Thank you," the waiter said. "Have a mce day. "

      The man took the bag and walked to a park.  He sat down and opened the bag.  He was surprised.

There was no hamburger or chips; there was only money in the bag-two thousand

dollars!  Where was the man's lunch?  Why was the money in the bag?

      The manager of the fast-food restaurant needed to go to the bank. He put two thousand

dollars in an envelope, He put it in a bag and put the bag down. The waiter gave the manager's

bag to the man by mistake. So the manager had a hamburger, chips and a coke, and the man had

two thousand dollars !

1. The man went to a restaurant to______.              

A. buy his lunch        

B. have a rest          

C. sell drinks        

D. cook food

2. The man wanted to have his lunch______.             

A. in a hotel          

B. in a shop            

C. in a restaurant      

D. in a park

3. When the man opened the bag, he found______in it.

A. food    

B. drink   

C. money   

D. nothing

4. How much money was there in the man's bag?

A. $ 100.    

B. $ 200.    

C. $ 100.    

D. $ 2,000.

5. ______ couldn't find his money.

A. The man    

B. The manager    

C. The waiter   

D. Nobody

单项选择题