问题 计算题

在如图所示的直角坐标系中,x轴的上方存在与x轴正方向成45°角斜向右下方的匀强电场,场强的大小为E=×104 V/m.x轴的下方有垂直于xOy面向外的匀强磁场,磁感应强度的大小为B=2×10-2 T.把一个比荷为=2×108 C/kg的正电荷从坐标为(0,1)的A点处由静止释放.电荷所受的重力忽略不计.

(1)求电荷从释放到第一次进入磁场时所用的时间;

(2)求电荷在磁场中做圆周运动的半径;(保留两位有效数字)

(3)当电荷第二次到达x轴时,电场立即反向,而场强大小不变,试确定电荷到达y轴时的位置坐标.

答案

(1)10-6 s (2)0.71 m (3)(0,8)

(1)如图,电荷从A点匀加速运动到x轴上C点的过程:

位移s=AC=m

加速度a==2×1012 m/s2

时间t==10-6 s.

(2)电荷到达C点的速度为

v=at=2×106 m/s

速度方向与x轴正方向成45°角,在磁场中运动时

由qvB=

得R=m

即电荷在磁场中的偏转半径为0.71 m.

(3)轨迹圆与x轴相交的弦长为Δx=R=1 m,所以电荷从坐标原点O再次进入电场中,且速度方向与电场方向垂直,电荷在电场中做类平抛运动.

设电荷到达y轴的时间为t′,则:

tan 45°=

解得t′=2×10-6 s

则类平抛运动中垂直于电场方向的位移

L=vt′=4 m

y==8 m

即电荷到达y轴时位置坐标为(0,8).

填空题

阅读短文,根据短文内容及首字母提示,在空白处填入一个适当的单词。

       Ron, the teacher at the skydiving (跳伞运动) school, was surprised when the gray-haired man said that his

name was Walter and asked if he could take skydiving lessons. Ron asked him how old he was and he

(1) r           that he was 60. Ron explained to Walter that (2) a            over 50 had to be checked by a doctor

before he could learn to jump from a plane. "I'm sorry, but I can't let you start learning (3) w            a letter

from your doctor."

       Walter smiled. "Here is a letter from my doctor. He asked me to take (4) l             of tests and he says that

I'm fine."

       So Walter was able to join the skydiving school. He came to all the lessons and worked very (5) h          .

Soon it was the time for him to make his (6) f             jump. Ron asked him if he was feeling OK. Walter

answered that he had never felt better. However, he added that there was something he should have told Ron

(7) e           . Ron asked what it was and Walter smiled. Then just before he jumped, he told Ron that he wasn't

60. Ron asked how old Walter (8) r            was and Walter told him he was 75!

       Walter has a lot of (9) h           . He enjoys riding fast motorbikes and (10) c            mountains. Last year

he was saved by a police helicopter (直升飞机) in Wales.

       His daughter Betty worries about him. "I think he should stop all these activities. But my mother says that

as long as he's happy, it's OK."

解答题