问题 问答题

如图甲所示,M、N为水平放置的平行板电容器的两个极板,两极板间距d=0.1m,两极板间的电压U=12.5V,O为上极板中心的小孔.以O为坐标原点,在y=0和y=2m之间有沿着x轴方向的匀强电场,PQ为电场区域的上边界,在x轴方向范围足够大.电场强度的变化如图乙所示,取x轴正方向为电场正方向.现有一个带负电的粒子,在t=0时刻从紧靠下极板中心O′,处无初速释放,经过小孔O进入交变电场中.粒子的比荷

q
m
=1×102C/kg,不计粒子重力,求粒子:

(1)进入交变电场时的速度;

(2)在8×10-3s末的位置坐标;

(3)离开交变电场时的速度大小和方向.

答案

(1)粒子运动至小孔O的速度为v0

由动能定理得qU=

1
2
m
v20

代入数据得v0=

2qU
m
=50m/s

(2)粒子从O′运动到O所用的时间为:

t0=

2d
v0
=4×10-3s

即自t=4×10-3s开始,粒子垂直射入交变电场,在t=4×10-3s~8×10-3s内,粒子做类平抛运动

在y方向上,粒子做匀速运动,

y=v0△t=50×4×10-3m=0.2m

在x方向上,粒子向右匀加速运动的加速度大小

a=

qE
m
=4×103m/s2

粒子向右运动的位移

x=

1
2
at2=
1
2
×4×103×(4×10-3)2m=3.2×10-2m

所以粒子在t=8×10-3s末的位置坐标为(0.032m,0.2m)

(3)由图可知,交变电场的变化周期T=8×10-3s,

粒子在交变电场中,在y方向上,一直做匀速运动,在x方向上,一直向右运动,先匀加速,再匀减速至静止,这样周期运动下去.

粒子在交变电场中运动的时间为t=

y
v0
=4×10-2s=5T

故粒子在离开交变电场时的水平速度为0

因此,粒子离开交变电场时的速度v=v0=50m/s,方向竖直向上.

答:(1)进入交变电场时的速度v0=50m/s;

(2)在8×10-3s末的位置坐标(0.032m,0.2m);

(3)离开交变电场时的速度大小为50m/s和方向竖直向上.

单项选择题
问答题

Mr. Vice Premier, the Finance Minister,
Mr. Mayor, Ladies and Gentlemen,
Let me, first of all, return the compliment, on behalf of all of us, to you, Mr. Vice Premier, to you, Mr.Minister, and you, Mr. Mayor, for the great contribution that you have made to the success of this meeting. Idon’t think any of us could have imagined a more well-organized conference or a more warm welcome thanyou have given us here in Shanghai, and I would like everyone to join me in expressing our thanks to you.[TONE]∥[TONE]
I would like to make just two general comments.
The first is that all of us have to work politically to ensure that poverty and the alleviation of poverty arecentral on the global agenda. I believe that today it is not central on the global agenda. I believe that todaylip service is given to the question of poverty. The real issues today that seem to be on the mind of theworld—terrorism, Iraq, Afghanistan, the budget deficits—are the visible problems that must be dealt with,that are immediate, while attention is given less to the equally inevitable and the equally dangerous problemsthat come with poverty. [TONE]∥[TONE]
We must deal with the question of social equity and social justice. Because without dealing with thatquestion of poverty, there can’t be any peace, and $900 billion being spent on military expenditure, $300billion being spent on agricultural subsidies, and $50- or $60 billion being spent on overseas developmentassistance is one of the absurdities that we have to change. [TONE]∥[TONE]
And the second and last thing I’d like to say is that we have talked about economics, we have talkedabout advances that must be made for social justice, and we’ve talked about steps that need to be taken inempowerment and in the methodologies that we can use to scale up. [TONE]∥[TONE]
But the one thing that we have not talked about and that I think all of us need to recognize is that if weare to be effective in advocating the case for poverty reduction, and hopefully eradication, is that we have to do it with a sense of belief that what we are doing is right. We should be addressing the question of poverty not just from economics, but because dealing with equity and social justice is right. [TONE]∥[TONE]
We should not be afraid to say that there is a human content in what we’re doing, but there is alsoa moral and, if you like, spiritual content in what we’re doing. We are not here just as economists. Weare here because we owe every human being in the world an opportunity and a chance to fulfill theirdestiny. [TONE]∥[TONE]
And so going out from this meeting I hope we feel a little bit uplifted and a little bit responsible to goout from here to deal with the question of scaling up of poverty alleviation because it’s right, and as membersof the human race, it’s something that we should do.
Thank you very much to our hosts, and thank you all for being here. [TONE]∥[TONE]