问题 问答题

设在地面上方的真空室内存在匀强电场和匀强磁场.已知电场强度和磁感应强度的方向是相同的,电场强度的大小E=4.0伏/米,磁感应强度的大小B=0.15特.今有一个带负电的质点以v=20米/秒的速度在此区域内沿垂直场强方向做匀速直线运动,求此带电质点的电量与质量之比

q
m
以及磁场的所有可能方向(角度可用反三角函数表示).

答案

根据带电质点做匀速直线运动的条件,得知此带电质点所受的重力、电场力和洛仑兹力的合力必定为零.由此推知此三个力在同一竖直平面内,如右图所示,质点的速度垂直纸面向外.

解法一:由合力为零的条件,可得:

mg=q

(vB)2+E2
…①

求得带电质点的电量与质量之比

q
m
=
g
(vB)2+E2
…②

代入数据得:

q
m
=
9.80
(20×0.15)2+4.02
C/kg=1.96C/kg…③

因质点带负电,电场方向与电场力方向相反,因而磁场方向也与电场力方向相反.设磁场方向与重力方向之间夹角为θ,则有

qEsinθ=qvBcosθ,

解得:tgθ=

vB
E
=
20×0.15
4
=0.75,θ=arctg0.75…④

即磁场是沿着与重力方向夹角θ=arctg0.75,且斜向下方的一切方向.

解法二:因质点带负电,电场方向与电场力方向相反,因而磁砀方向也与电场力方向相反.设磁场方向与重力方向间夹角为θ,由合力为零的条件,可得:

qEsinθ=qvBcosθ…①

qEcosθ+qvBsinθ=mg…②

解得:

q
m
=
g
(vB)2+E2
…③

代入数据得:

q
m
=1.96C/kg…④

tgθ=

vB
E
=
20×0.15
4
=0.75,θ=arctg0.75…⑤

即磁场是沿着与重力方向成夹角θ=arctg0.75,且斜向下方的一切方向.

答:此带电质点的电量与质量之比

q
m
为1.96C/kg,磁场是沿着与重力方向成夹角θ=arctg0.75,且斜向下方的一切方向.

阅读理解

阅读理解

     Everyone has his own birthday. People in different countries celebrate(庆祝) their birthdays  in 

different ways. Here are four people from different countries. They will tell us how they celebrate their

birthdays in their countries.

     Sandy Morrison comes from Madrid(马德里). He says happily, " My twenty-first birthday is on a

Saturday, and I'm going to go out with some friends. To wish me a happy birthday, they are going to

pull(拉, 扯) on my ear twenty-one times, once for each year. It is an old custom(风俗). Some people

pull on the ear just once, but my friends are very traditional."

     Mr. and Mrs. Sato are from Tokyo. Mr. Sato is going to be sixty tomorrow. In Japan, the sixtieth

birthday is called Kanreki-it's the beginning of a new life. The colour red is for a new life, so they

always, give something red for a sixtieth birthday. Mrs. Sato says, " What am I going to give my

husband. I can't say. It's a surprise(惊喜). "

     Li Xiaomei from Beijing feels very excited and tells us, " Tomorrow is my sixteenth  birthday. It's a

special birthday. So we're going to have a family party. I'm probably going to get some money in lucky

envelopes(信封) from my relatives. My mother is going to cook noodles noodles are for a long life."

     Phillip  Evans, from Paris, smiles to us, " I'm going to be thirty next week, so I'm going to invite three

very good friends out to dinner. In France, when you have birthday, you often invite people out. In some

countries, I know it's the opposite-people take you out."

1. Do people in different countries celebrate their birthdays in the same way?

                                                              

2. Is Mr. Sato going to receive something red on his birthday?

                                                                

3. What is Li Xiaomei going to do on her birthday?

                                                                

4. How old is Phillip Evans going to be?

                                                                

5. Who is going to take his friends out to dinner on his birthday?

                                                                

单项选择题