题目内容
如图所示,在xoy 坐标平面的第一象限内有一沿y 轴正方向的匀强电场,在第四象限内有一垂直于平面向内的匀强磁场,现有一质量为m带电量为q的带负电粒子(重力不计)从电场中坐标为(3L,L)的P点沿x轴负方向以速度
射入,从O点沿着与y轴正方向成
夹角射出,求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241314300283951.png)
小题1:粒子在O点的速度大小.
小题2:匀强电场的场强E.
小题3:粒子从P点运动到O点所用的时间.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131429966325.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131429997393.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241314300283951.png)
小题1:粒子在O点的速度大小.
小题2:匀强电场的场强E.
小题3:粒子从P点运动到O点所用的时间.
小题1:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131430044615.png)
小题2:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131430075796.png)
小题3:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131430106749.png)
(1)粒子运动轨迹如图所示,设粒子在P点时速度大小为
,OQ段为四分之一圆弧,QP段为抛物线,根据对称性可知,粒子在Q点的速度大小也为
,方向与x轴正方向成450.可得
(2)Q到P过程,由动能定理得
即
(3)在Q点时,
由P到Q过程中,竖直方向上有:
水平方向有:
则
OQ = 3L-2L = L
得粒子在OQ段圆周运动的半径
Q到O的时间:
P到O t=" "![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131430106749.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131430137265.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131430137265.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131430231705.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131430044615.png)
(2)Q到P过程,由动能定理得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131430293954.png)
即
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131430075796.png)
(3)在Q点时,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131430652787.png)
由P到Q过程中,竖直方向上有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131430668592.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241314306995178.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131430746810.png)
水平方向有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131430777633.png)
OQ = 3L-2L = L
得粒子在OQ段圆周运动的半径
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131430808603.png)
Q到O的时间:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241314308391032.png)
P到O t=" "
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131430106749.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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