题目内容
(14分)如图所示,在直角坐标系的第一、四象限内有垂直于纸面的匀强磁场,第二、三象限内有沿x轴正方向的匀强电场,电场强度大小为E,y轴为磁场和电场的理想边界. 一个质量为m,电荷量为e的质子经过x轴上A点时速度大小为
,速度方向与x轴负方向夹角θ=30º. 质子第一次到达y轴时速度方向与y轴垂直,第三次到达y轴的位置用B点表示,图中未画出,已知OA=l,不计质子重力影响.
(1)求磁感应强度的大小和方向;
(2)求质子从A点运动至B点时间.![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241204062432551.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120406227210.gif)
(1)求磁感应强度的大小和方向;
(2)求质子从A点运动至B点时间.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241204062432551.jpg)
(1)
,垂直纸面向里(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120406274672.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120406258540.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120406274672.gif)
⑴由于质子第一次到达y轴时速度方向与y轴垂直,因此粒子在磁场中一定是逆时针旋转,由左手定则可判断磁场方向垂直纸面向里。从
到达
轴速度的偏转角为30°,由几何关系得轨道半径
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120406305523.gif)
由牛顿第二定律得![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120406321553.gif)
解得磁感应强度![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120406336510.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241204063675705.jpg)
⑵质子从
到达
轴的时间![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120406648662.gif)
进入电场后做匀减速直线运动,加速度![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120406664437.gif)
运动时间![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120406679644.gif)
再次进入磁场后做匀速圆周运动,经半个周期又到达
轴,运动时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120406711594.gif)
总时间![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120406726666.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120406289202.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120406305199.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120406305523.gif)
由牛顿第二定律得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120406321553.gif)
解得磁感应强度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120406336510.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241204063675705.jpg)
⑵质子从
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120406289202.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120406305199.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120406648662.gif)
进入电场后做匀减速直线运动,加速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120406664437.gif)
运动时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120406679644.gif)
再次进入磁场后做匀速圆周运动,经半个周期又到达
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120406305199.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120406711594.gif)
总时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120406726666.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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