如图所示，在边长为L的等边三角形ACD区域内，存在磁感应强度为B、方向垂直纸面向外的匀强磁场。现有一束质量为m、电荷量为+q的带电粒子，以某一速度从AC边中点P、平行于CD边垂直磁场射入，粒子的重力可忽略不计。
(1)若粒子进入磁场时的速度大小为v0，求粒子在磁场中运动的轨道半径；
(2)若粒子能从AC边飞出磁场，求粒子在磁场中运动的时间；
(3)为使粒子能从CD边飞出磁场，粒子进入磁场时的速度大小应满足什么条件？
解：(1)设粒子在磁场中运动的轨道半径为r，则
解得
(2)粒子在磁场中运动的周期
在磁场中运动的时间
而
解得
(3)设粒子从CD边飞出磁场的最小半径为r1，对应最小速度为v1，则
解得
设粒子能从D点飞出磁场，对应的半径为r2，速度为v2，圆心角为α，则
解得
α=60°
由几何关系可知，粒子能从D点飞出磁场，且飞出时速度方向沿AD方向
由于
解得
所以速度大小应满足的条件
完形填空（共15小题；每小题1分, 满分15分） Wings of Angel I used to hate myself because I wasn’t “normal”. Everyone else could play on the monkey bars and ride on a bicycle, but not 37 . I had a severe spinal cord disorder (脊髓病) and I knew I would always be much 38 than others. I hated going to school and I hated people 39 at me. I hated seeing others smiling broadly and standing straight and tall. And most of all, I hated looking in the 40 and seeing an ugly hunchback (驼背). My friends found me distant because I didn’t let others get 41 to me. I thought I was going to go on like this for the rest of my life 42 Angela appeared. That afternoon, I was sitting by myself in a corner of the school — a spot where no one would 43 me. That’s when I first heard her voice. “Hi. Can I sit down?” I raised my head and there she was, with an irresistible smile on her round face. “What are you looking at?” she asked. “Ants.” “What are they doing?” “No idea.” “I bet they’re playing games and making friends. Don’t you think so?” That was how our 44 started and it didn’t stop. We talked about everything under the sun—the ants, the clouds, my situation — until it was sunset. Then suddenly, she saw my 45 . She just stared. My heart sank. What I feared most had happened and I knew for sure she would 46 me now. She stood up, pointed at my back and said, “I know 47 your back is hunched.” I closed my eyes like a criminal waiting to be sentenced(审判). I begged in my heart for her to 48 , but she just kept on going. “I know what you’ve got in there. Do you?” “No,” I answered weakly. She bent and 49 my ears. “Your back is hunched because you’ve got a pair of wings from the angels.” I was 50 .I looked into her eyes and her kindness touched my heart. From that day on, I started to learn to 51 myself because I have the wings of an angel and a kind-hearted friend.
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