两屏幕荧光屏互相垂直放置，在两屏内分别去垂直于两屏交线的直线

问题计算题

两屏幕荧光屏互相垂直放置，在两屏内分别去垂直于两屏交线的直线为x和y轴，交点O为原点，如图所示。在y>0，0<x<a的区域有垂直于纸面向内的匀强磁场，在y>0，x>a的区域有垂直于纸面向外的匀强磁场，两区域内的磁感应强度大小均为B。在O点出有一小孔，一束质量为m、带电量为q（q>0）的粒子沿x周经小孔射入磁场，最后打在竖直和水平荧光屏上，使荧光屏发亮。入射粒子的速度可取从零到某一最大值之间的各种数值。已知速度最大的粒子在0<x<a的区域中运动的时间与在x>a的区域中运动的时间之比为2︰5，在磁场中运动的总时间为7T/12，其中T为该粒子在磁感应强度为B的匀强磁场中做圆周运动的周期。试求两个荧光屏上亮线的范围（不计重力的影响）。

答案

对于y轴上的光屏亮线范围的临界条件如图1所示：带电粒子的轨迹和x=a相切，此时r=a，y轴上的最高点为y="2r=2a " ;

对于 x轴上光屏亮线范围的临界条件如图2所示：左边界的极限情况还是和x=a相切，此刻，带电粒子在右边的轨迹是个圆，由几何知识得到在x轴上的坐标为x=2a;速度最大的粒子是如图2中的实线，又两段圆弧组成，圆心分别是c和c’ 由对称性得到 c’在 x轴上，设在左右两部分磁场中运动时间分别为t1和t2,满足

解得由数学关系得到：

代入数据得到：

所以在x 轴上的范围是

完形填空。
Learning experiences happen to us throughout our lives.Not long ago,I had one that I would like to__1__.I was going to Marblehead with my sailboat team.The team was racing down the highway at 85 mph__2__,we realized we were__3__.Luckily,we saw a rest area ahead.I had a brand-new (崭新的)$20 bill.I was so__4__ because I had never had that kind of cash before.But spending it on__5__seemed like throwing it away.We all rushed into the pizza line.__6__I got a pizza and a drink,and walked to my table.About halfway through the meal,I__7__I had not actually handed any money to the cashier.I had just__8__out,and nobody had noticed.I felt terrible. My conscience(良心)opened its mouth and swallowed me in one big bite.I couldn’t__9__ over it.I just couldn’t go back to the cashier and__10__for my stolen pizza.I was so upset that I __11__ to give myself the pleasure of an ice cream for __12__that someone would say,“Hey,Jeff,why don’t yo u use the change __13__ the pizza instead of that nice,new $20 bill?” I was not __14__of my cash now. For the next two years,whenever I was __15__of the “pizza incident”,I would say to myself,“Don’t think about it...” I have learned two things from this __16__.Maybe I was a fool for __17__in to my conscience,and being too stupid to appreciate a __18__pizza.But the real lesson is that even if you get away from what you have done your conscience will __19__ up with you. This reflects the saying,“A coward (懦夫)dies a thousand deaths,a hero dies one.” I was a coward and have felt terrible about that incident at least a thousand times.If I had been a “__20__” and gone back to pay for the pizza,I would have felt a little uncomfortable about it only once,or maybe twice.
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