如图所示，半径为R的绝缘圆筒中有沿轴线方向的匀强磁场，磁场方_爱下问搜题

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问题计算题

如图所示，半径为R的绝缘圆筒中有沿轴线方向的匀强磁场，磁场方向垂直于纸面向里，匀强磁场的磁感应强度为B，圆筒形场区的边界由弹性材料构成。一个质量为m．电荷量为q的正离子(不计重力)以某一速度从筒壁上的小孔M进入筒中，速度方向与半径成θ=30°夹角，并垂直于磁场方向。离子和筒壁的碰撞无能量和电荷量的损失．若选择合适的进入速度，离子可以从M孔射出。问：

(1)离子的速度多大时，离子可以在最短的时间内返回M孔最短的时间是多少?

(2)如果离子与筒壁发生两次碰撞后从M孔射出，离子的速率是多大?从进入圆筒到返回M孔经历的时间是多少?

答案

(1) (2)

(1)离子要在最短的时间内返回M孔，离子只能与圆筒碰撞一次，据此画出离子的运动轨迹如图所示，碰撞点在过M点的直径的另一端N。设离子在磁场中的轨迹半径为r，速率为V₁.根据向心力公式,①结合图中的几何关系可得r=2R，②解得离子的速率,③离子在磁场中走过的每段圆弧对应的圆心角=60°，④经历的时间,⑤即.⑥

(2)离子与筒壁发生两次碰撞后从M孔射出，根据对称性画出离子的运动轨迹如图所示。

结合图中的几何关系可得r=R， ⑦

则离子的速率， ⑧

离子在磁场中走过的每段圆弧对应的圆心角′=120°， ⑨

经历的时间。 ⑩

解答题

2010年圣诞节（12月25日）是星期六，那么2011年的圣诞节是星期几？

阅读理解

A very little boy was spending his Saturday morning playing in his sandbox. He had with him a plastic pail (桶) and a shiny, red plastic shovel (铲). In the  1  of creating roads and tunnels in the sand, he   2  a large rock in the middle of the sandbox.
The boy dug around the rock, 3  to move it off the dirt. At first, he wanted to carry it out of the sandbox with his hands; however, it was too heavy. Later, with much   4 , he pushed the rock across the sandbox by   5 his hands. When the boy got the rock to the   6  of the sandbox, he found that he couldn’t roll it up and   7  the little wall.   8 , the little boy pushed, but every time he thought he had made some   9 , the rock tipped (翻滚) and then fell back into the sandbox. The little boy pushed and pushed, but his only   10  was to have the rock roll back.
Finally he 11  tears. All this time the boy’s father watched from his living room window   12  the drama was unfolded. The moment the tears fell, a large   13  appeared across the sandbox. It was the boy’s father. Gently but   14 , he said, “Son, why didn’t you use all the strength that you had?”
Defeated, the boy   15  back, “I did! I did! I used all the strength that I had!”
“No, you didn’t. You didn’t ask me for help.” The father   16  down, picked up the rock and dropped it off the sandbox.
Do you have “rocks” in your life that need to be   17 ? Are you discovering that you don’t have   18  it takes to lift them? There is someone who is willing to give us the 19  we need. Maybe, it’s sometimes a good idea to ask others for   20  when we meet difficulties we can’t overcome.

D．controlling

D．rushed into

A．surprisingly