问题 问答题

如图所示,ABCDEF是一边长为L的正六边形盒,各边均为绝缘板,盒外有方向垂直纸面向里、范围足够大的匀强磁场,磁感应强度大小为B.在盒内有两个与AF边平行的金属板M、N,且金属板N靠近盒子的中心O点,金属板M和盒子AF边的中点均开有小孔,两小孔与O点在同一直线上.现在O点静止放置一质量为m、电荷量为q的带正电粒子(不计粒子的重力).

(1)如果在金属板N、M间加上电压UNM=U0时,粒子从AF边小孔射出后直接打在A点,试求电压U0的大小.

(2)如果改变金属板N、M间所加电压,试判断粒子从AF边小孔射出后能否直接打在C点.若不能,说明理由;若能,请求出此时电压UNM的大小.

(3)如果给金属板N、M间加一合适的电压,粒子从AF边小孔射出后恰好能以最短时间回到该小孔(粒子打在盒子各边时都不损失动能),试求最短时间.

答案

(1)依题意,R=

L
4

由qvB=m

v2
R

及qU0=

1
2
mv02

解得U0=

qB2L2
32m

(2)设AF中点为G,连接GC,作其垂直平分线,与AF延长线交点即为圆心

由相似三角形得R′=O′G=

13L
4

由牛顿第二定律,qvB=

mv2
R

∵qU0=

1
2
mv02

∴UNM=

169qB2L2
32m

(3)由于粒子在磁场中运动周期T=

2πm
qB
,T与速率无关粒子撞击BC中点和DE中点后回到G,

用时最短圆周半径R″=

3
2
L,

得到最短时间t=

300
360
T×3=
5πm
qB

答:(1)如果在金属板N、M间加上电压UNM=U0时,粒子从AF边小孔射出后直接打在A点,则电压U0的大小U

qB2L2
32m

(2)如果改变金属板N、M间所加电压,试判断粒子从AF边小孔射出后能否直接打在C点.若不能,说明理由;若能,此时电压UNM的大小

169qB2L2
32m

(3)如果给金属板N、M间加一合适的电压,粒子从AF边小孔射出后恰好能以最短时间回到该小孔,则最短时间为

5πm
qB

阅读理解

Bobby was sitting out in his back yard in the snow. The thin sneakers he wore had a few holes in them. Try as he might, he could not come up with an idea for his mother’s Christmas gift.

Ever since his father had passed away three years ago, his mother worked nights at the hospital, but the small wage could only be stretched so far.

What the family lacked in money and material things, they more than made up for in love and family unity. They ran the household in their mother’s absence. All three of his sisters had already made beautiful gifts for their mother.

It was Christmas Eve already, and he had nothing. Bobby started to walk down to the street. He walked from shop to shop. Everything seemed so beautiful and so out of reach. It was starting to get dark, then suddenly his eyes caught a shiny dime. Never has anyone felt so wealthy as Bobby did at that moment.

He went inside a flower shop. When the owner asked if he could help him, Bobby presented the dime and asked if he could buy one flower. The shop owner looked at Bobby, then said, “You just wait here and I’ll see what I can do for you.”

The shop owner returned holding red roses all tied together with a big silver bow. Bobby’s heart sank as the owner placed them gently into a long white box. “That will be ten cents, young man,” said the shop owner, reaching out his hand for the dime. Slowly, Bobby moved his hand to give the man his dime.

Then the shopkeeper’s wife appeared. “Where are the roses you were fixing?”

The shop owner replied, “A strange thing happened to me this morning. I thought I heard a voice telling me to set aside a dozen of my best roses for a special gift. I wasn’t sure at the time whether I had lost my mind or what, but I set them aside anyway. When I saw that little boy tonight, I knew who that voice was.”

小题1:According to the first three paragraphs we know that _____.

A.Bobby’s sisters didn’t help Bobby to buy a gift

B.Bobby had known what gift he’d give to his mother

C.the children in the family all loved their mother

D.Bobby’s family was rich before his father died小题2:Why did Bobby walk along the street?

A.Because he didn’t know what to do.

B.Because he wanted to try his luck there.

C.Because he wanted to get some money.

D.Because he hoped to see what he could get.小题3:What could he buy with a dime then?

A.A flower.

B.Nothing.

C.A piece of cake.

D.Many flowers.小题4:Bobby slowly gave the dime to the shop owner because _______.

A.he did not want any rose flowers

B.the flowers weren’t worth a dime

C.the shop owner would cheat him

D.he hardly believed what had happened小题5:From the last two paragraphs we can infer that the shop owner ______.

A.was shocked by the voice he heard

B.was always ready to help others

C.didn’t know how to run a business

D.was good at making up stories

判断题