问题 计算题

在光滑绝缘的xOy平面内,有甲、乙、丙三个区域,在x<0的甲区域内存在着方向沿x轴正方向的匀强电场,该电场区电场强度,在0≤x<a的区域内有磁感应强度为B=0.5 T,方向垂直于xOy平面向里的匀强磁场,在x≥a、y>0的区域内有匀强电场,电场强度的大小是甲区域的π倍。现有一带正电的小球自平面上坐标原点O以沿-x轴方向的初速度v0射向甲电场区,,已知在甲区域和乙区域内粒子运动的时间是相等的,粒子进入丙区域时的电场力与其速度垂直,且后来粒子通过了x轴,又已知粒子的带电荷量q=0.1 C,粒子的质量m=10-2 kg,试求:

(1)a的数值;

(2)粒子在丙区域内运动的时间。

答案

解:(1)粒子进入甲区域做类竖直上抛运动 ①

则粒子在甲区域运动的时间 ②

粒子在乙区域做匀速圆周运动,设其运动半径为R,运动周期为T,则 ③

 ④

则由③④得,  ⑤

设粒子在通过乙区域时速度的偏转角为θ,因粒子在乙区域运动的时间和甲区域相等,故 ⑥

由②⑤⑥得 ⑦

在粒子进入丙区域的C点处作y轴的垂线交y轴于D,过C作该点速度的垂线交y轴于O',则△DO'C中有a=Rsinθ ⑧

解得a=3π=9.42 m

(2)粒子进入丙区域后做类平抛运动,由题知其场强方向应沿O'C斜向下,将O'C反向延长交x轴于H,过粒子在丙区域的轨迹与x轴的交点F作O'C反向延长线的垂线得垂足为G,设粒子在丙区域运动的时间为t2

 ⑨

GF=v0t2

又在△HGF中有

 

解⑨⑩

阅读理解

   Gao Xiaosong, who is a famous musician, movie director and the writer of the famous song My Deskmate,

has been sent to jail (监狱) and will stay there for six months for drunk driving.

   "I've nothing to say for myself and I'm willing to be punished (惩罚)," he said when he was standing in the

court. "What I want to say is that I feel sorry for what I've done. I thought alcohol (酒精) could bring me

freedom but never realized drunk driving could take away others' freedom. And now I've lost my own freedom

because of drinking. I'll obey the new road safety rules and I want to be a life-long volunteer in persuading

(劝说) others not to drive after drinking."

   Anyone who drives after drinking doesn't think much of human life. If Gao had cared, he would have left his

car parked outside the restaurant and took a taxi home, and he would have thought about a road killer he would

become. It's fair to say that his behavior can not be excused in modern society. Gao may not have killed anyone, but by choosing to drive a car while under the influence of alcohol, he and the large number of others who do

the same have made the dangerous decision that may possibly hurt other people.

1. What was the reason for Gao Xiaosong's being jailed for six months?

   ________________________________________________________

2. How did he feel for what he had done?

   ________________________________________________________

3. Did he think he was wrong?

   ________________________________________________________

4. If one drives after drinking, what may happen?

    _______________________________________________________

5. What's your idea after reading this passage?

   ________________________________________________________

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