问题 问答题

如图所示,在x轴上方有一匀强电场,场强大小为E,方向竖直向下.在x轴下方有一匀强磁场,磁感应强度为B,方向垂直于纸面向里.在x轴上有一点p,离原点距离为a.现有一带电量为+q,质量为m的粒子,不计重力,从0<x<a区间某点由静止开始释放后,能经过p点.试求:

(1)释放瞬间粒子的加速度;

(2)释放点的坐标x、y应满足的关系式?

答案

(1)要使粒子从静止开始能经过P点,其初始位置必须在匀强电场区域里,根据牛顿第二定律得:

    释放瞬间粒子的加速度为a=

qE
m
,方向沿y轴负方向.

(2)由于粒子从0<x<a区间某点由静止开始释放,轨迹如图.

由于粒子可能偏转一个、十个…半圆到达P点,由几何知识得

    a-x=2nR(n=1,2,3,…)①

设释放处距O的距离为y,则有

qEy=

1
2
mv2 ②

又 qvB=m

v2
R
  ③

联立①②③得 y=

B2q(a-x)2
8n2mE
(n=1,2,3,…)

答:

(1)释放瞬间粒子的加速度为

qE
m
,方向沿y轴负方向.

(2)释放点的坐标x、y应满足的关系式y=

B2q(a-x)2
8n2mE
(n=1,2,3,…).

单项选择题 A1型题
单项选择题

Weak dollar or no, $ 46,000-the price for a single year of undergraduate instruction amid the red brick of Harvard Yard-is (1) But nowadays cost is (2) barrier to entry at many of America’s best universities. Formidable financial-assistance policies have (3) fees or slashed them deeply for needy students. And last month Harvard announced a new plan designed to (4) the sticker-shock for undergraduates from middle and even upper-income families too.

Since then, other rich American universities have unveiled (5) initiatives. Yale, Harvard’s bitterest (6) , revealed its plans on January 14th. Students whose families make (7) than $60,000 a year will pay nothing at all. Families earning up to $ 200,000 a year will have to pay an average of 10% of their incomes. The university will (8) its financial- assistance budget by 43%, to over $ 80m.

Harvard will have a similar arrangement for families making up to $180,000. That makes the price of going to Harvard or Yale (9) to attending a state-run university for middle-and upper-income students. The universities will also not require any student to take out (10) to pay for their (11) , a policy introduced by Princeton in 2001 and by the University of Pennsylvania just after Harvard’s (12) . No applicant who gains admission, officials say, should feel (13) to go elsewhere because he or she can’t afford the fees.

None of that is quite as altruistic as it sounds. Harvard and Yale are, after all, now likely to lure more students away from previously (14) options, particularly state-run universities, (15) their already impressive admissions figures and reputations.

The schemes also provide a (16) for structuring university fees in which high prices for rich students help offset modest prices for poorer ones and families are less (17) on federal grants and government-backed loans.

Less wealthy private colleges whose fees are high will not be able to (18) Harvard or Yale easily. But America’s state-run universities, which have traditionally kept their fees low and stable, might well try a differentiated (19) scheme as they raise cash to compete academically with their private (20) . Indeed, the University of California system has already started to implement a sliding-fee scale.

1()

A.cheap

B.reasonable

C.high

D.expensive