问题 问答题

一平行板电容器的两个极板ab、cd正对竖直放置,如图所示,极板长为L.现有一电荷量大小为q、质量为m的带电质点P自紧靠ab板内侧的某点以大小为v的初速度竖直向上射出,然后以速度v从cd板的上端c处水平进入cd板右侧的正交电场、磁场中并恰好做匀速圆周运动;当带电质点P运动到cd板上小孔O处时,有另一带电质点Q由静止释放,P、Q两带电质点在小孔处发生正碰,已知Q的质量为m/3,碰撞前Q的电性与P相同且电荷量大小为q/2,碰撞后Q运动到ab板内侧的最下端b处时仍以大小为v的速度竖直离开电容器.忽略平行板电容器两端电场的边缘效应.求:

(1)电容器两板间的电场强度大小;

(2)磁场的磁感应强度大小;

(3)带电质点P最后离开平行板电容器时的速度大小.

答案

(1)设P从出发点运动至c阶段运动的时间为t.

其中水平加速度为ax,则在水平方向上有:ax=

qE
m
…①

v=axt=

qE
m
t…②

在竖直方向上有:0-v=-gt…③

t=

v0
g
…④

联立①②③得:E=

mg
q
…⑤

(2)设电容器两极板间的距离为d.

对P从出发点至c阶段,在水平方向上有:d=

v+0
2
t…⑥

联立④⑥解得d=

v2
2g
…⑦

设在正交电场、磁场中质点P做匀速圆周运动的半径为R,则qvB=m

v2
R

R=

mv
qB
…⑧

又2R+d=l…  ⑨

联立⑦⑧⑨得:B=

4mgv
q(2gl-v2)

(3)设P、Q碰撞后的速度分别为v1、v2

由动量守恒定律得,mv=mv1+

m
3
v2

设碰撞后P、Q带电量大小分别为q1、q2,则q1+q2=

3
2
q

碰撞后Q在水平方向上有:d=

v2+0
2
t

可得:v2=v,v1=

2
3
v

0-v22=-2

q2E
m
3
d

q1=

7
6
q,q2=
q
3

则碰撞后P在水平方向上的加速度ax=

q1E
m
=
7
6
g.

它在电容器中间运动的时间仍为t,设P射出电容器时其水平速度为vx

vx=v1-axt=-

1
2
v

则P射出电容器时的速度为vp

vp=

vx2+v2
=
5
2
v.

答:(1)电容器两板间的电场强度为

mg
q

(2)磁场的磁感应强度大小为

4mgv
q(2gl-v2)

(3)带电质点P最后离开平行板电容器时的速度大小为

5
2
v.

填空题
单项选择题

It may be just as well for Oxford University’s reputation that this week’s meeting of Congregation, its 3,552-p governing body, was held in secret, for the air of civilized rationality that is generally supposed to pervade donnish conversation has lately turned fractious. That’s because the vice-chancellor, the nearest thing the place has to a chief executive, has proposed the most fundamental reforms to the university since the establishment of the college system in 1249; and a lot of the dons and colleges don’t like it.

The trouble with Oxford is that it is unmanageable. Its problems-the difficulty of recruiting good dons and of getting rid of bad ones, concerns about academic standards, severe money worries at some colleges-all spring from that. John Hood, who was recruited as vice-chancellor from the University of Auckland and is now probably the most-hated antipodean in British academic life, reckons he knows how to solve this, and has proposed to reduce the power of dons and colleges and increase that of university administrators.

Mr. Hood is right that the university’s management structure needs an overhaul. But radical though his proposals seem to those involved in the current row, they do not go far enough. The difficulty of managing Oxford stems only partly from the nuttiness of its system of governance; the more fundamental problem lies in its relationship with the government. That’s why Mr. Hood should adopt an idea that was once regarded as teetering on the lunatic fringe of radicalism, but these days is discussed even in polite circles. The idea is independence.

Oxford gets around £5,000 ($9,500) per undergraduate per year from the government. In return, it accepts that it can charge students only £1,150 (rising to£3,000 next year) on top of that. Since it probably costs at least £10,000 a year to teach an undergraduate, that leaves Oxford with a deficit of £4,000 or so per student to cover from its own funds.

If Oxford declared independence, it would lose the £52m undergraduate subsidy at least. Could it fill the hole Certainly. America’s top universities charge around £20,000 per student per year. The difficult issue would not be money alone, it would be balancing numbers of not-so-brilliant rich people paying top whack with the cleverer poorer ones they were cross-subsidising. America’s top universities manage it: high fees mean better teaching, which keeps competition hot and academic standards high, while luring enough donations to provide bursaries for the poor. It should be easier to extract money from alumni if Oxford were no longer state-funded.

It is implied in the third paragraph that ()

A. reliance upon official subsidy has bred the current predicament of Oxford

B. an overhaul of Oxford management structure is urgently needed

C. the nuttiness of Oxford system of governance may be easily removed

D. the current row is essential to many in polite circle