题目内容
(12分)如图所示,在纸平面内建立如图所示的直角坐标系xoy,在第一象限的区域存在沿y轴正方向的匀强电场。现有一质量为m、电量为e的电子从第一象限的某点P(
)以初速度v0沿x轴的负方向开始运动,经过
轴上的点Q(
)进入第四象限,先做匀速直线运动然后进入垂直纸面的矩形匀强磁场区域,其左边界和上边界分别与y轴、x轴重合,电子经磁场偏转后恰好经过坐标原点O并沿y轴的正方向运动,不计电子的重力。求
(1)电子经过Q点的速度
;
(2)该匀强磁场的磁感应强度
;
(3)该匀强磁场的最小面积S。![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241218241195013.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121823714355.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121823729187.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121823885282.gif)
(1)电子经过Q点的速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121824088185.gif)
(2)该匀强磁场的磁感应强度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121824104206.gif)
(3)该匀强磁场的最小面积S。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241218241195013.jpg)
(1)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121824322284.gif)
(2)
,方向垂直纸面向里
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121824540346.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121824322284.gif)
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121824525606.gif)
(3)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121824540346.gif)
(1)电子类平抛运动, ![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121824556489.gif)
解得 ![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121824728495.gif)
所以经过Q点的速度![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121824852675.gif)
方向与水平方向夹角为![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241218248681001.gif)
(2)速度偏转角为
,则圆弧所对的圆心角为
。
由几何关系得
解得 ![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121825055402.gif)
由向心力公式
解得 ![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121824525606.gif)
方向垂直纸面向里。………………
(3)矩形磁场的右边界距y轴的距离为![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121825102684.gif)
矩形磁场的下边界距x轴的距离为![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121825055402.gif)
故磁场的最小面积为![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121824540346.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121824556489.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121824728573.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121824728495.gif)
所以经过Q点的速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121824852675.gif)
方向与水平方向夹角为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241218248681001.gif)
(2)速度偏转角为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121824884254.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121824884254.gif)
由几何关系得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121824946575.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121825055402.gif)
由向心力公式
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121825071873.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121824525606.gif)
方向垂直纸面向里。………………
(3)矩形磁场的右边界距y轴的距离为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121825102684.gif)
矩形磁场的下边界距x轴的距离为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121825055402.gif)
故磁场的最小面积为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121824540346.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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