问题 问答题

矩形裸导线框长边的长度为2l,短边的长度为l,在两个短边上均接有阻值为R的电阻,其余部分电阻均不计.导线框的位置如图所示,线框内的磁场方向及分布情况如图,大小为B=B0cos(

πx
2l
).一电阻为R的光滑导体棒AB与短边平行且与长边始终接触良好.起初导体棒处于x=0处,从t=0时刻起,导体棒AB在沿x方向的外力F的作用下做速度为v的匀速运动.试求:

(1)导体棒AB从x=0运动到x=2l的过程中外力F随时间t变化的规律;

(2)导体棒AB从x=0运动到x=2l的过程中整个回路产生的热量.

答案

(1)在t时刻AB棒的坐标为x=vt

导体棒产生的感应电动势 e=Blv=B0lvcos

πvt
2l

回路的总电阻 R=R+

1
2
R=
3
2
R

回路感应电流 i=

e
R
=
2B0lvcos2
πvt
l
3R

棒匀速运动时有F=F=Bil

解得:F=

2
B20
l2vcos2(
πvt
2l
)
3R
(0≤t≤
2l
v
)

(2)导体棒AB在切割磁感线的过程中产生半个周期的正弦交流电

感应电动势的有效值为 E=

2
2
B0lv

回路产生的电热Q=

E2
R
t

通电时间t=

2l
v

联立解得Q=

2
B20
l3v
3R

答:

(1)导体棒AB从x=0运动到x=2l的过程中外力F随时间t变化的规律为F=

2
B20
l2vcos2(
πvt
2l
)
3R
(0≤t≤
2l
v
)

(2)导体棒AB从x=0运动到x=2l的过程中整个回路产生的热量为

2
B20
l3v
3R

阅读理解

A city in California has got some new buses. They cost $490,000 each. The new buses are different from the old ones. These new buses are better for the environment. They are called hybrid (混合动力的) buses. They run on diesel (柴油的) and electric power. This will help keep the air cleaner.

The man drove the new bus on Wednesday and noticed a difference right away. “I get to have clean air for a change”, said driver Melvin Day. “I’m smelling diesel all day long when I drive the old ones.”

The company that builds the buses had many good things to say about them. For example, they said they use a lot less fuel (燃料). They also said that they are 90% cleaner for the environment. The buses are very quiet, too.

The buses have a diesel engine in the back and batteries (电池) on top. When the engine starts up, it is powered by electricity. Then the diesel power takes over.

Over time the city would like to use the new hybrid buses instead of all 50 of their buses. They hope to do this over the next three years. The city will give money to help buy the new kind of buses.

One other bit of good news: the price of the bus ticket will not rise because of the new buses.

小题1:Why are the new buses better for the environment?

A.Because they’re cheaper than the old ones.

B.Because they are very quiet.

C.Because they run on diesel and electric power.

D.Because they are new.小题2:Which one is NOT TRUE about the new buses?

A.They use a lot less fuel.

B.They can drive faster than the old ones.

C.They will help keep the air cleaner.

D.The buses are very quiet.小题3:How many buses does the city have now?

A.490.

B.90.

C.45.

D.50.小题4:Which one is TRUE about this article?

A.The driver liked the new buses very much.

B.The new buses don’t use fuel at all.

C.The city will replace the old buses in a year.

D.The price of bus ticket will be high.小题5: What is the best title for the article?

A.The New Cars.

B.Electric Buses.

C.The Advantages of Electric Buses.

D.Buying New Buses.

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