题目内容
如图所示,在直角坐标系的第一、二象限内有垂直于纸面的匀强磁场,第三象限有沿
轴负方向的匀强电场;第四象限无电场和磁场。现有一质量为
、电荷量为
的粒子以速度
从
轴上的
点沿
轴负方向进入电场,不计粒子的重力,粒子经
轴上的
点和
点最后又回到
点,设
,
,求:
(1)带电粒子的电性,电场强度
的大小;
(2)带电粒子到达
点时的速度大小和方向;
(3)匀强磁场的磁感应强度的大小和方向;
(4)粒子从
点进入电场,经
、
点最后又回到
点所用的时间?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603015295.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603031333.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603078297.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603124305.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603015295.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603156384.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603234262.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603234262.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603280342.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603296288.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603156384.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603343528.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603358545.png)
(1)带电粒子的电性,电场强度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603405311.png)
(2)带电粒子到达
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603280342.png)
(3)匀强磁场的磁感应强度的大小和方向;
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241136036084391.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603156384.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603280342.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603296288.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603156384.png)
(1)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603764850.png)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603873557.png)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603967838.png)
(4)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241136040291185.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603764850.png)
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603873557.png)
(3)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603967838.png)
(4)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241136040291185.png)
(1)粒子从
至
运动过程有:
,加速度:
,运动时间:
,电场强度
,则:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603764850.png)
(2)设
与
成
角,则
,
,带电粒子到
点速度:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603873557.png)
(3)带电粒子在磁场中做圆周运动的轨迹如图所示,圆心在
处,设半径为
,由几何关系知带电粒子过
点的速度方向与
成
角,则![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113604840631.png)
则:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113604887625.png)
由牛顿第二定律得:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113604965899.png)
解得:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603967838.png)
(4)粒子从
至
时间:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113605059608.png)
粒子在磁场中运动时间:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241136051061356.png)
粒子从
至
运动时间![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113605184849.png)
从
点进入电场,经
、
回
所用时间![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241136040291185.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603156384.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603280342.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113604138625.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113604154653.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113604185586.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241136042481127.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603764850.png)
(2)设
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113604279352.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603234262.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113604388284.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113604404867.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113604435449.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603280342.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603873557.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241136046226216.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113604638321.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113604684316.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603296288.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603234262.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113604778363.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113604840631.png)
则:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113604887625.png)
由牛顿第二定律得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113604965899.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603967838.png)
(4)粒子从
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603156384.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603280342.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113605059608.png)
粒子在磁场中运动时间:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241136051061356.png)
粒子从
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603296288.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603156384.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113605184849.png)
从
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603156384.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603280342.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603296288.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113603156384.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241136040291185.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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