题目内容
(15分)如图所示,在xoy坐标系内存在周期性变化的电场和磁场,电场沿y轴正方向,磁场垂直纸面(以向里为正),电场和磁场的变化规律如图所示。一质量
、电荷量
的带电粒子,在t=0时刻以
的速度从坐标原点沿x轴正向运动,不计粒子重力。求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082413490954310473.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082413490957412672.png)
(1)粒子在磁场中运动的周期;
(2)
时粒子的位置坐标;
(3)
时粒子的速度。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134909309826.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134909387736.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134909496646.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082413490954310473.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082413490957412672.png)
(1)粒子在磁场中运动的周期;
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134909792632.png)
(3)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134909824659.png)
(1)
(2)(9.6×10-2m,-3.6×10-2m)(3)10m/s
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134909933538.png)
(1)粒子在磁场中运动时
(2分)
(1分)
解得
(1分)
(2)t=20×10-3s时粒子在坐标系内做了两个圆周运动和三段类平抛运动
水平位移
(1分)
竖直位移
(1分)
Eq=ma (1分)
y=3.6×10-3s
故t=20×10-3s时粒子的位置坐标为(9.6×10-2m,-3.6×10-2m)(1分)
(3)t=24×103s时粒子的速度大小、方向与t=20×103s时相同,设与水平方向夹角为a(1分)
(1分)
uy=3aT (1分)
tana=
(1分)
解得u=10m/s (1分)
与x轴正向夹角a为37º(或arctan
)斜向右下方 (1分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134909964801.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134910042691.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241349100891071.png)
(2)t=20×10-3s时粒子在坐标系内做了两个圆周运动和三段类平抛运动
水平位移
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134910136987.png)
竖直位移
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134910167815.png)
Eq=ma (1分)
y=3.6×10-3s
故t=20×10-3s时粒子的位置坐标为(9.6×10-2m,-3.6×10-2m)(1分)
(3)t=24×103s时粒子的速度大小、方向与t=20×103s时相同,设与水平方向夹角为a(1分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134910214666.png)
uy=3aT (1分)
tana=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134910260481.png)
解得u=10m/s (1分)
与x轴正向夹角a为37º(或arctan
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134910370385.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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