问题 计算题

如图甲所示,M和N是相互平行的金属板,OO1O2为中线,O1为板间区域的中点,P是足够大的荧光屏,带电粒子连续地从O点沿OO1方向射入两板间。

(1)若只在两板间加恒定电压U,M和N相距为d,板长为L(不考虑电场边缘效应)。若入射粒子是电量为e、质量为m的电子,试求能打在荧光屏P上偏离点O2最远的电子的动能。

(2)若两板间只存在一个以O1点为圆心的圆形匀强磁场区域,磁场方向垂直纸面向里,已知磁感应强度B=0.50T,两板间距d=cm,板长L=1.0cm,带电粒子质量m=2.0×10-25 kg,电量q=8.0×10-18 C,入射速度v=×105m/s。若能在荧光屏上观察到亮点,试求粒子在磁场中运动的轨道半径r,并确定磁场区域的半径R应满足的条件。

(3)若只在两板间加如图乙所示的交变电压u,M和N相距为d,板长为L(不考虑电场边缘效应)。入射粒子是电量为e、质量为m的电子。某电子在t0=时刻以速度v0射入电场,要使该电子能通过平行金属板,试确定U0应满足的条件。

答案

解:(1)电子在两极板间的加速度

通过金属板的时间

对打在荧光屏P上偏离点O2最远的粒子有

此时粒子的动能

联列解得

(2)由牛顿第二定律可知

代入数据解得

如图所示,设恰好在荧光屏P上观察到亮点时,粒子偏转角为2θ,磁场区域的最大半径为R0,由几何关系可知

代入数据解得

则R应满足的条件

(3)交变电压的周期,则

电子通过金属板的时间

电子在两极板间的加速度

设电子分别在时间内沿垂直于初速度方向运动的位移依次为y1、y2、y3、y4,则有

要使电子能通过平行金属板,应满足条件

联列解得

口语交际,情景问答题
阅读理解

阅读理解。

     In general, people talk about two groups of colors: warm colors and cool colors. Researchers in

psychology think that there are also two groups of people: people who prefer warm colors and people

who prefer cool colors.

    The warm colors are red, orange and yellow. Where there are warm colors and a lot of light, people

usually want to be active. People think that red, for example, is exciting. Sociable people, those who like

to be with others, like red. The cool colors are green, blue and violet. These colors, unlike warm colors,

are relaxing. Where there are cool colors, people are usually quiet. People who like to spend time alone

often prefer blue.

    Red may be exciting, but one researcher says that time seems to pass more slowly in a room with

warm colors than in a room with cool colors. He suggests that a warm color, such as red or orange is a

good color for a living room or restaurant. People who are talking or eating do not want time to pass

quickly. Cool colors are better for offices or factories if the people who are working there want time to

pass quickly.

    Researchers do not know why people think some colors are warm and other colors are cool.

However, almost everyone agrees that red, orange, and yellow are warm and that green, blue, and violet

are cool. Perhaps warm colors remind people of warm days and the cool colors remind them of cool

days. Because in the north the sun is higher during summer, the hot summer sunlight appears yellow. 

1. Which of the following colors belong to cool colors?  

A. Yellow, green.      

B. Blue, violet. 

C. Black, blue.        

D. Brown, white. 

2. Which of the following statements is not true?   

A. Sociable people like warm colors. 

B. Warm colors can make people excited. 

C. People who like to be with others don't like red. 

D. Where there are warm colors, people want to be active. 

3. Which is the right color for different rooms?    

A. Red or orange for offices.  

B. Orange for dining-rooms. 

C. Blue for bedrooms.      

D. Red for studies. 

4. What is the main idea of the last paragraph? 

A. It shows the reason why people think some colors are warm and others are cool. 

B. Warm colors remind people of warm days.

C. Cool colors remind people of cool days.

D. People have an agreeable opinion of warm colors and cool colors.