问题 计算题

(18分)如图所示,在y轴左侧有一匀强电场,场强大小为E,方向与x轴平行且沿x轴正向,在y轴右侧有一匀强磁场,方向垂直纸面向外。现将一挡板放在第一象限内,其与x、y轴的交点M、N到坐标原点的距离均为2L。有一质量为m电荷量为+q的粒子在第二象限内从距x轴为L、y轴为4L的P点由静止释放(不计重力),粒子与挡板碰后电荷量不变,速度大小不变方向变为沿y轴正向,当粒子第一次到达y轴时电场消失。求:

(1)粒子第一次到达y轴时距坐标原点多远?

(2)若使粒子再次打到档板上,磁感应强度的大小的取值范围?

答案

(1)(2)≤B≤     

(1)设粒子与板作用前瞬间,速率为,由动能定理有

      (1分)

        (1分)

粒子与档板碰后在电场中作类平抛运动,设到达y轴时与Q点的竖距离为y,

在x轴方向有 (1分)

在y轴方向有   (1分)

由以上二式得 (1分)

            (1分)

故粒子第一次到达y轴时距坐标原点为              (1分)

(2)粒子到A点时,x轴方向的速度分量为 (1分)

与y轴正向的夹角为有,,故         (1分)

此时速度                          (1分)

粒子进入磁场后将做匀速率圆周运动,转过300°后打到板上的N点时,磁感强度为最大,有                     (1分)

                                               (1分)

=                          (1分)

当磁感强度的大小减小到时,粒子做半径为r2的圆周运动到达y轴上的C点,之后沿直线运动打到板上的M点。

∠OCM=30°,OC长为                              (1分)

                                             (1分)

同理                          (1分)

所以B的取值范围为:≤B≤              (2分)

本题考查的是带电粒子在磁场和电场中运动的规律问题,首先根据动能定理计算出初速度,再根据带电粒子在电场中运动的规律计算出第一次到达y轴时距离原点的距离;最后根据粒子在磁场中运动的规律计算出磁感应强度的取值范围;

阅读理解

Depression (抑郁症) is a serious problem today.Depression causes workers to be unproductive,causing companies and countries to lose billions of dollars.One expert says that depression is like cancer because it is “widespread,costly and deadly”.Depression hits one person in five around the world.

Although people have believed depression to be a problem among the rich and educated,studies show that depression is a problem among everyone.Over any six­month period,between five to seven percent of the world’s population will be suffering from a serious depression.Suicide rates among people suffering from the disease in its extreme,or clinical form were 80 percent higher than in the population at large,and sufferers were four times more likely to have heart attacks.People who suffer from depression often have problems sleeping,getting up on time,and doing work productively.

Depression,which researchers agree has its origin in the genes,brings loss of confidence and ability to concentrate—making it impossible for employees and managers to work efficiently.

Depression is made more serious in China by Chinese’s inability to face it.Many people believe that depressed people are either weak or lazy.Besides,there is no good treatment,with few specialists available.“Most patients in China just don’t get help,”a Chinese doctor says.“In my hospital,I have to see 30 or 40 patients in a morning,just have time to say ‘Hello,how do you feel?’”

In Western countries,people are not afraid to admit that they have depression,but most do not tell it to their boss,because they fear that they will be stricken_off_the_rolls.“In my experience,aging bosses are the most willing to admit they have it.Because they feel the most secure about themselves,” an American doctor says.

Hopefully,in the near future,people around the world will be able to admit that they have depression so that they can get the right treatment.

小题1:Which of the following is true according to the passage?

A.It is widely believed that everyone may suffer from depression.

B.Depression brings great problems to its sufferers in their life and work.

C.Depression is a commonly­existing problem only in rich countries.

D.The poorer and the less educated a person is,the less he will suffer from depression.小题2:.Compared to normal people,the depressed people are likely to be________.

A.very unconfident and often absent­minded

B.easy to avoid being hit by heart attacks

C.working efficiently and productively

D.either weak or lazy小题3:Depression becomes more serious in China because of________.

A.the understanding of the problem

B.the lack of treatment and doctors

C.their unwillingness to tell it to their boss

D.the doctors’ careless work小题4:What can we infer from the passage?

A.People are suffering from depression because of the shortage of specialists.

B.The aging bosses around the world dare to say they are depressed.

C.More and more patients will turn to specialists for help.

D.Western people are braver than Chinese people.小题5:What does the underlined words in the 5th paragraph mean?

A.Hired.

B.Dismissed.

C.Promoted. 

D.Recommended.

单项选择题