题目内容
如图甲所示,在光滑绝缘的水平桌面上平放着相互平行、间距为0.1m的金属板
、
,板间存在匀强电场,方向水平向右. 在
板右侧平面内存在如图乙所示的交替变化的电磁场. 以
板小孔处为坐标原点,建立
坐标系,且规定沿
方向为电场的正方向,竖直向下为磁场的正方向. 在
点一质量为10g、电荷量为0.1C的带正电的金属小球由静止释放,设
时刻金属小球恰好以
m/s的速度经小孔进入
板右侧. 已知
N/C、
=0.2
T. 求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241700538774584.png)
(1)
、
两板间的电场强度
的大小;
(2)在1s~2s内,金属小球在磁场中做圆周运动的半径和周期;
(3) 前6s内金属小球运动至离
轴的最远点的位置坐标.(计算结果可以含
)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170048978297.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170049477304.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170049477304.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170049477304.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170050835447.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170051069331.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170051287386.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170051490348.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170051693439.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170049477304.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170052270535.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170053081361.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170053502309.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241700538774584.png)
(1)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170048978297.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170049477304.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170055125320.png)
(2)在1s~2s内,金属小球在磁场中做圆周运动的半径和周期;
(3) 前6s内金属小球运动至离
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170055546266.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170053502309.png)
(1)2N/C(2)1s
(3)
, ![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241700572461031.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170056310620.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170056653854.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241700572461031.png)
试题分析:(1)由动能定理得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170057511870.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170057761336.png)
(2)0s~1s内,小球做类平抛运动,在1s末
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170058198331.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170058463815.png)
合速度大小为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170058697649.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170058900378.png)
在1s~2s内,小球做匀速圆周运动,设半径为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170059883327.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170100257865.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170056310620.png)
由
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170101006817.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170101333393.png)
(3)小球的轨迹如图所示,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241701016924860.png)
在5s末小球的坐标为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170102082706.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170102457975.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170102878341.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241701032831415.png)
方向与
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170055546266.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170103658292.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241701040321273.png)
在5s~6s内,小球做圆周运动半径为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241701042041042.png)
运动至圆周的最高点
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170104594306.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170104999742.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170105467927.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170105686690.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170106076851.png)
点评:这类问题的关键在于能够将粒子的轨迹准确无误的画出。通过类平抛运动得到解决问题的关键。通过轨迹找出求解的等式。
![](http://thumb2018.1010pic.com/images/loading.gif)
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