问题 计算题

在真空室内速度为v=6.4×107m/s的电子束连续地沿两平行导体极板的中心线射入,如图所示,极板长L=8.0×10-2m,两极板间距离d=5.0×10-3m,两极板不带电时,电子束将沿中心线射出极板。今在两极板间加上50Hz的交变电压U=U0sin100πtV,发现有时有电子从两极板之间射出,有时则无电子从两极板间射出,若有电子射出的时间间隔与无电子射出的时间间隔之比△t1:△t2=2:1,则所加的交变电压的最大值U0为多大?已知电子的质量为m=9.1×10-31kg,电量为e=1.6×10-19C。

答案

105V.

题目分析:电子飞出电场的时间,交变电压的周期T=0.02s;

t远小于T,电子相当于穿过一个恒定的电场,做类平抛运动.电子恰好不能通过电场时电压为Uc,则电子飞出电场的时间:

联立得:

代入解得,Uc=91V

因为电子通过的时间t1跟间断的时间t2之比为△t1:△t2=2:1,所以在半个周期内,将有

的时间极板间电压的瞬时值超过UC=91V,而的时间内极板间电压的瞬时值小于UC=91V.根据正弦交流电的变化规律可知,应有:UC=U0sin() 代入解得:U0=105V.

单项选择题
单项选择题

Many people who work in London prefer to live outside it, and to go in to their offices or schools every day by train, car or bus, even though this means they have to get up early in the morning and reach home late in the evening.

One advantage of living outside London is that houses are cheaper. Even a small flat in London without a garden costs quite a lot to rent. With the same money, one can get a little house in the country with a garden of one’s own.

Then, in the country one can rest from the noise and hurry of the town. Even though one has to get up earlier and spend more time in trains or buses, one can sleep better at night and during weekends and on summer evenings, one can enjoy the fresh, clean air of the country. If one likes gardens, one can spend one’s free time digging, planting, watering and doing the hundred and one other jobs which are needed in a garden. Then, when the flowers and vegetables come up, one has the reward of one who has shared the secret of Nature.

Some people, however, take no interest in country things: for them, happiness lies in the town, with its cinemas and theatres, beautiful shops and busy streets, dance-halls and restaurants. Such people would feel that their life was not worth living if they had to live it outside London. An occasional walk in one of the parks and a fortnight’s (two weeks) visit to the sea every summer is all the country they want: the rest they are quite prepared to leave to those who are glad to get away from London every night.

One can use the same money for () to buy a little house with a garden in the country.

A. getting a small flat with a garden

B. having a small flat with a garden

C. renting a small flat without a garden

D. buying a small flat without a garden