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辽宁省2023~2024学年度下学期高一期中考试(24606A)数学.考卷答案试卷答案
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18.(16分)如图所示,在xOy平面内,有两个半圆形同心圆弧,与坐标轴分别交于a,b、c点和a'、b'、C点,其中圆弧a'b'c的半径为R..两个半圆弧之间的区域内分布着辐射状的电场,电场方向由原点O向外辐射,其间的电势差为U.圆弧a'b'上方圆周外区域,存在着上边界为y=2R的垂直纸面向里的足够大匀强磁场,圆弧abe内无电场和磁场.O点处有一粒子源,在xOy平面内向x轴上方各个方向,射出质量为m,,电荷量为的带正电的粒子,带电粒子射出时的速度大小均为2gUm,被辐射状的电场加速后进人磁场,不计粒子的重力以及粒子之间的相互作用,不考虑粒子从磁场返回圆形区域边界后的运动.求:(1)粒子被电场加速后的速度(2)要使粒子能够垂直于磁场上边界射出磁场,求磁场的磁感应强度的最大值B0;(3)当磁场中的磁感应强度大小为第(2)问中B0的的32倍时,求能从磁场上边界射出粒子的边界宽度L.
