问题 计算题

(18分)如图所示,真空中有以(r,0)为圆心,半径为r的圆柱形匀强磁场区域,磁场的磁感应强度大小为B,方向垂直于纸面向里,在y=r的实线上方足够大的范围内,有方向水平向左的匀强电场,电场强度的大小为E,从O点向不同方向发射速率相同的质子,质子的运动轨迹均在纸面内,设质子在磁场中的偏转半径也为r,已知质子的电量为e,质量为m,不计重力及阻力的作用,求:

(1)质子射入磁场时的速度大小。

(2)速度方向沿x轴正方向射入磁场的质子,到达y轴所需的时间。

(3)速度方向与x轴正方向成30°角(如图所示)射入磁场的质子,到达y轴的位置坐标。

答案

(1)(2)(3)

题目分析:(1)质子进入匀强磁场做匀速圆周运动,洛伦兹力提供向心力即

可得

(2)速度方向沿x轴正方向射入磁场的质子运动轨迹也是半径r的圆周,根据洛伦兹力方向判断圆心在y轴上,根据几何关系可得在匀强磁场中运动四分之一圆周,垂直于电场的方向进入匀强电场,轨迹如下图

匀强磁场中圆周运动周期,那么此磁场中运动的时间

离开磁场进入匀强电场后,初速度竖直向上,电场力水平向左,为类平抛运动,

水平方向初速度0的匀加速直线运动:

时间

到达y轴所需的时间即

(3)速度方向与x轴正方向成30°角 射入磁场的质子,磁场中运动轨迹仍是半径r的圆周,根据洛伦兹力提供向心力轨迹如图

根据几何关系四边形是菱形,根据几何关系转过的圆心角为从C点离开磁场垂直电场线进入电场。

C点到y轴的距离

质子进入电场后仍是类平抛运动

水平方向

竖直方向匀速直线运动,电场中竖直方向位移

质子进入电场前Y轴方向位移为半径r

质子到达y轴的位置为

所以到达Y轴的坐标位置为

阅读理解

Rae and Bruce Hostetler not only work very hard,they also relax just as well. Numerous vacations help the couple to maintain their health and emotional well-being一and it’s no surprise to health care professionals.

“Rest, relaxation, and stress reduction are very important for people’s well-being and health. This can be accomplished through daily activities, such as exercise and meditation, but vacation is an important part of this as well,” said primary care physician Natasha Withers from One Medical Group in New York. Withers lists a decreased risk of heart disease and improved reaction time as some of the benefits from taking some time off. “We also know that the mind is very powerful and can help with healing, so a rested, relaxed mind is able to help the body heal better,” said Withers.

Psychologists confirm the value of vacations for the mind. “The impact that taking a vacation has on one’s mental health is great,” said Francine Lederer, a clinical psychologist in Los Angeles who specializes in stress and relationship management. “Most people have better life perspective and are more motivated to achieve their goals after a vacation, even if it is a 24- hour time-out.” The trips could be good for their health, good for their family and good for their businesses.

The online travel agency Expedia conducted a survey about vacation time in 2010, and according to their data the average American earned 18 vacation days一but only used 14 of them. France topped the list, with the average worker earning 37 vacation days and using all but two of them. Americans, responses may not be surprising in a culture where long hours on the job often are valued, but that’s not always good for the individual, the family or the employer.

Psychologists have also found that people who don’t take enough time to relax may find it harder to relax in the future. “Without time and opportunity to do this, the nerve connections that produce feelings of calm and peacefulness become weaker, making it actually more difficult to shift into less-stressed states,” Mulhem said.

小题1:How did the author introduce the topic of the text?

A.By making comparisons.

B.By giving an example.

C.By raising questions.

D.By providing data.小题2:Expedia’s survey shows that Americans _____.

A.dislike family gatherings

B.have the shortest vacation

C.enjoy as many vacations as the French

D.think much of spending long hours on the job小题3:What can be inferred from the last paragraph?

A.One should never wait to relax.

B.Work and rest go against each other.

C.Time and opportunity wait for no man.

D.A relaxed mind determines everything.

单项选择题