问题 问答题

如图所示,平面直角坐标系的y轴竖直向上,x轴上的P点与Q点关于坐标原点O对称,距离为2a.有一簇质量为m、带电量为+q的带电微粒,在xoy平面内,从P点以相同的速率斜向右上方的各个方向射出(即与x轴正方向的夹角θ,0°<θ<90°),经过某一个垂直于xoy平面向外、磁感应强度大小为B的有界匀强磁场区域后,最终会聚到Q点,这些微粒的运动轨迹关于y轴对称.为使微粒的速率保持不变,需要在微粒的运动空间再施加一个匀强电场.重力加速度为g.求:

(1)匀强电场场强E的大小和方向;

(2)若一个与x轴正方向成30°角射出的微粒在磁场中运动的轨道半径也为a,求微粒从P点运动到Q点的时间t;

(3)若微粒从P点射出时的速率为v,试推导微粒在x>0的区域中飞出磁场的位置坐标x与y之间的关系式.

答案

(1)由题意知,要保证微粒的速率不变,则微粒所受电场力与重力平衡:

                 qE=mg…①

   解得:E=

mg
q
…②方向竖直向上

  (2)设A、C分别为微粒在磁场中运动的射入点和射出点,根据题意画出微粒的运动轨迹如图所示根据几何关系可得:

           

AC
=
360°
2πa…③

           PA=

a
cosθ
atanθ…④

设微粒运动的速率为v,由牛顿定律:

              qvB=m

v2
a
…⑤

微粒从P点运动到Q运动的路程为s,则:

              s=2PA+

AC
AC…⑥

               t=

s
v

联解③④⑤⑥得:

          t=

(2
3
+π)m
3qB
…⑦

(3)根据题意作出粒子在x>0区域内的运动示意如图所示,设微粒飞出磁场位置为C,在磁场中运动的轨道半径为r,根据牛顿定律和几何关系可得:

           qBv=m

v2
r
…⑧

              x=rsinθ…(⑨

      y=(

a
cosθ
-rtanθ)sinθ   …⑩

联解(⑧⑨⑩)得:

    y=

Bq(ax-x2)
m2v2-B2q2x2
…(14)

答案为:(1匀强电场场强:E=

mg
q
,方向竖直向上

       (2)微粒从P点运动到Q点的时间:t=

(2
3
+π)m
3qB

        (3微粒在x>0的区域中飞出磁场的位置坐标x与y之间的关系式:y=

Bq(ax-x2)
m2v2-B2q2x2

选择题
阅读理解

阅读理解

     As the world watched the twin towers of the World Trade Center come under attack, a common phrase was repeated: "It looks like a movie."

     But this time there was no superman to save the people or the famous building. The attack destroyed one of the world's highest skyscrapers and left 5,000 people dead or missing.

     Movie fans have become used to such events after years of Hollywood films showing disasters, terrorism(恐怖主义) and danger, The Empire State Building, the White House, New York City and even the American president himself have all been threatened by terrorist attacks in these exciting films.

     The film "True Lies", released(发行) in 1994 is considered to be a good example of this kind of movie. The special effects, including explosions and missiles, make the action look like a real thing.

     "Independence Day" in 1996 took this type of movie one step further by blowing up the White House.   This science fiction movie is about a war between human beings and aliens(外来人) from another planet. In the movie, the World Trade Center towers are destroyed.

     Violence has become a major part of Hollywood movies. And this is what people enjoy. Soon after the attacks, many famous film companies stopped the planned releases of some of their new movies, especially if their films showed terrorist attacks or plane crashes. "Swordfish" was top of the American box office in June, 2001. But the movie's story was frighteningly similar to the Sept.11 disaster. The film would have been stopped in American and British cinemas after the attack.

     But it's unlikely that Hollywood will stay quiet for long. It is already waiting for the feeling in America to calm down.

1. What is the main subject of the newspaper article?

A. The relationship between the Sept.11 attack and Hollywood films.

B. The effect of the Sept.11 attack on Hollywood films

C. The response Hollywood made to the Sept.11 attack.

D. The result of Hollywood films showing violence and disasters.

2. Which of the following is true?

A. Hollywood made a lot of money out of the film "Swordfish" in June.

B. Hollywood stopped making films showing terrorism and disasters after the  Sept.11 attack.

C. "Swordfish" was not allowed to be shown after the Sept.11 attack.

D. The World Trade Center was destroyed because no superman came to save it.

3. From this article we know that       .

A. Hollywood is a filmmaking center making films of violence and disasters

B. too many Hollywood films showing terrorism and disasters resulted in the  Sept.11 attack

C. people who were used to the Hollywood films were not shocked at the Sept.11 attack.

D. in fact, the Sept.11 attack had nothing to do with Hollywood films.