题目内容
如图所示,在x>0的空间中,存在沿x轴正方向的匀强电场E;在x<0的空间中,存在沿x轴负方向的匀强电场,场强大小也为E;一电子(电荷量大小为e、质量为m)在x=d处的P点以沿y轴正方向的初速度v0开始运动,不计电子重力。求:
(1)电子第一次到达y轴时的坐标
(2)电子沿y轴正方向分运动的周期![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241219549114039.jpg)
(1)电子第一次到达y轴时的坐标
(2)电子沿y轴正方向分运动的周期
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241219549114039.jpg)
(1)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121954927833.gif)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121954943734.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121954927833.gif)
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121954943734.gif)
(1)电子在电场中运动的受力情况及轨迹如图所示(略)。在
的空间中,沿y轴正方向以v0的速度做匀速直线运动,沿x轴负方向做匀加速直线运动,设加速度的大小为a,
则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121955005438.gif)
解得,
即电子第一次到达Y轴时的坐标![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121954927833.gif)
(2)电子从A点进入
的空间后,沿y轴正方向仍做v0的匀速直线运动,沿x轴负方向做加速度大小仍为a的匀减速直线运动,到达Q点。根据运动的对称性得,电子在x轴方向速度减为零的时间![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121955083217.gif)
,电子沿y轴正方向的位移![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121955130800.gif)
电子到达Q点后,在电场力作用下,运动轨迹 QCP1与QAP关于QB对称,而后的运动轨迹沿y轴正方向重复PAQCP1,所以有:电子的沿y轴正方向分运动的周期![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121954943734.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121954958244.gif)
则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121954974450.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121954989479.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121955005438.gif)
解得,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121955021591.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121955036676.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121954927833.gif)
(2)电子从A点进入
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121955067247.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121955083217.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121955021591.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121955130800.gif)
电子到达Q点后,在电场力作用下,运动轨迹 QCP1与QAP关于QB对称,而后的运动轨迹沿y轴正方向重复PAQCP1,所以有:电子的沿y轴正方向分运动的周期
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121954943734.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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