题目内容
如图所示,在正交坐标系
的空间中,同时存在匀强电场和匀强磁场(x轴正方向水平向右,y轴正方向竖直向上)。匀强磁场的方向与
平面平行,且与x轴的夹角为60°。一质量为m、电荷量为+q的带电质点从y轴上的点
沿平行于z轴方向以速度
射入场区,重力加速度为g。
(1)若B的大小不变,要使质点恰好做匀速圆周运动,求电场强度E的大小及方向;
(2)若B的大小可以改变,要使质点沿
方向做匀速直线运动,求电场强度E的最小值及方向;
(3)撤去磁场,而电场强度E仍为第(2)问所求的情况, 当带电质点从P点射入,求它运动到
平面时的位置坐标。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241344386172878.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134438212522.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134438258468.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134438321604.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134438383333.png)
(1)若B的大小不变,要使质点恰好做匀速圆周运动,求电场强度E的大小及方向;
(2)若B的大小可以改变,要使质点沿
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134438383333.png)
(3)撤去磁场,而电场强度E仍为第(2)问所求的情况, 当带电质点从P点射入,求它运动到
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134438555398.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241344386172878.png)
(1)
方向竖直向上(2)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241344387581060.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134438664660.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134438711781.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241344387581060.png)
(1)由于质点做匀速圆周运动,所以质点受到电场力、重力二力平衡,
即:
---------------(3分)
方向竖直向上 --------------------------------------(2分)
(2)当电场力方向与洛伦兹力方向垂直时,场强有最小值。
此时电场强度的方向与
平面的夹角为60°,即与磁感应强度B的方向相同。-----(2分)
------------------------------------(3分)
---------------------------------------------(2分)
(3)撤去磁场后,带电质点受到重力mg和电场力
作用,其合力与存在磁场时的洛伦兹力大小相等方向相反,与
方向垂直,做类平抛运动。设经过时间t到达
平面内的点
。
------------(2分)
y =" 0" --------------------------------(1分)
加速度a= gsin300 =" g/2" ---------(2分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134439335945.png)
(2分)
-------------------------(1分)
--------------------(1分)
-----(1分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241344395539046.jpg)
即:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134438804712.png)
方向竖直向上 --------------------------------------(2分)
(2)当电场力方向与洛伦兹力方向垂直时,场强有最小值。
此时电场强度的方向与
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134438555398.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134438882994.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134438960740.png)
(3)撤去磁场后,带电质点受到重力mg和电场力
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134439054531.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134438383333.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134438555398.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134439194708.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134439272855.png)
y =" 0" --------------------------------(1分)
加速度a= gsin300 =" g/2" ---------(2分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134439335945.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134439366540.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134439413485.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134439460705.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241344387581060.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241344395539046.jpg)
![](http://thumb2018.1010pic.com/images/loading.gif)
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