题目内容
如图甲所示,建立x0y坐标系,两平行极板P、Q垂直于y轴且关于x轴对称,极板长度和板间距均为L,第Ⅰ、Ⅳ象限分布着匀强磁场,方向垂直于x0y平面向里。位于极板左侧的粒子源可沿x轴向右发射质量为m、电量为q、速度相同、重力不计的带正电粒子。在0~3t0时间内两极板所加电压如图乙所示。已知,若粒子在t=0时刻射入,将恰好在t0时刻经极板边缘射入磁场。上述m、q、L、t0为已知量,且忽略粒子间的相互影响。求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250007215416691.png)
(1)电压U0的大小;
(2)匀强磁场的磁感应强度B;
(3)0~3t0时间内何时射入的粒子在磁场中运动的时间最短,并求出此最短时间。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250007215416691.png)
(1)电压U0的大小;
(2)匀强磁场的磁感应强度B;
(3)0~3t0时间内何时射入的粒子在磁场中运动的时间最短,并求出此最短时间。
(1)
(2)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000721588503.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000721556830.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000721572614.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000721588503.png)
试题分析:(1)根据t=0时刻进入两板间的带电粒子恰好在t0时刻经极板边缘射出,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000721619967.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000721556830.png)
(2)水平方向
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000721650486.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000721666678.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000721681455.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000721697497.png)
所以速度偏转角为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000721728362.png)
由几何关系可知
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000721744600.png)
由
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000721759747.png)
得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000721775906.png)
(3)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000721790408.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000721822465.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000721837870.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250007219006935.jpg)
![](http://thumb2018.1010pic.com/images/loading.gif)
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