问题 问答题

足够长且电阻不计的金属光滑导轨MN、PQ水平放置,导轨间距为d,M、P两点间接有阻值为R的电阻,建立平面直角坐标系,坐标轴x,y分别与PQ、PM重合,如图所示.空间存在垂直导轨平面且范围足够大的磁场,磁场沿x轴的分布规律为B=B0sin(

λ
x),其中B0、l 为常数,以竖直向下方向为B 的正方向.一根电阻不计的导体棒AB垂直导轨放置,在与棒垂直的水平外力F的作用下从非常靠近y轴的位置以速度v 匀速向x 轴的正方向运动,运动过程中,棒始终与导轨垂直.求:

(1)导体棒运动到哪些位置,回路中的电流达到最大值;

(2)外力随时间t的变化关系;

(3)导体棒发生上个λ的位移过程中,电阻R上产生的焦耳热.

答案

(1)导体棒切割磁感线产生的感应电动势为E=Bdv

感应电流为 I=

E
R
=
Bdv
R
=
B0dvsin(
λ
x)
R

则知 电流最大时导体棒的位置坐标为 x=

2n-1
4
λ(n=1,2,3…).

(2)导体棒所受的安培力 F=BId 

导体棒做匀速运动,外力与安培力平衡,则有 F=F=BId

 又 x=vt 

联立得 F=

vd2
R
B20
sin2(
λ
vt)

(3)由I=

dv
R
B0sin
λ
vt,可知该交流电为正弦交流电,则在导体棒发生一个λ的位移过程中,交流电变化了一个周期.产生的焦耳热为:

  Q=[

dv
R
B0
2
]2R•
λ
v
=
d2
B20
2R

答:

(1)导体棒运动到位置坐标为 x=

2n-1
4
λ(n=1,2,3…)时,回路中的电流达到最大值;

(2)外力随时间t的变化关系为F=

vd2
R
B20
sin2(
λ
vt).

(3)导体棒发生上个λ的位移过程中,电阻R上产生的焦耳热是

d2
B20
2R

单项选择题
阅读理解

阅读理解。

     You know the sound of your heartbeat: lub-dub, lub-dub. In some people, there's an extra noise that the

blood makes as it flows through the heart. It sounds sort of like the noise of flowing water. This sound is

called a murmur.

     Just like kids, murmurs have grades. Grade l is the softest-sounding murmur, and Grade 6 is the loudest.

A murmur graded 4, 5, or 6 is so loud you can actually feel a rumbling from it under the skin if you put your

hand on the person's chest.

     Most murmurs don't mean anything is wrong. Doctors may call these "innocent", "functional", or "normal"

murmurs.

     One common type of normal murmur is Still's murmur, named for the doctor who first described it. This

murmur is most often heard in healthy children aged 3 to 7.

     A normal murmur can get louder when the blood flows faster through the heart, like when kids have a

fever or run around. That's because an increase in body temperature or activity makes the heart pump more

blood. When your temperature goes down, the murmur may get quieter or even disappear.

     It can be easier to hear heart murmurs in kids because they have less fat, muscle, and bone between the

murmur and the doctor's stethoscope (听诊器). Many normal murmurs become harder to hear as children

grow older, and some eventually disappear.

     Even though most murmurs do not mean anything is wrong, sometimes a heart problem can cause a

murmur. If your doctor thinks your heart murmur could be due to a heart problem, you will need to see a

pediatric cardiologist. This kind of doctor knows a lot about children's hearts.

1. What's the text mainly about?

A. Heart problems.

B. Heart murmurs.

C. Murmur types.

D. Murmur grades.

2. We can hear a kid's louder heart murmur when he has just _____.

A. woken up from a sound sleep

B. listened to some light music

C. played football for two hours

D. finished reading a storybook

3. This text is most probably taken from _____.

A. a science magazine

B. an experiment report

C. a hospital introduction

D. a medical advertisement

4. We can learn from the last paragraph that _____.

A. most heart murmurs do harm to kids' health

B. some heart murmurs can cause heart problems

C. doctors know what has led to low temperatures

D. a certain heart problem can cause a heart murmur