题目内容
坐标原点O处有一放射源,它向xOy平面内的x轴下方各个方向发射速度大小都是v0的
粒子,
粒子的质量为m、电量为q;在0<y<d的区域内分布有指向y 轴正方向的匀强电场,在y≥d的区域内分布有垂直于xOy平面向里的匀强磁场,磁感应强度B=
,ab为一块很大的平面感光板,在磁场内平行于x轴放置,如图所示。测得进入磁场的a粒子的速率均为2v0,观察发现此时恰好无粒子打到ab板上。(
粒子的重力忽略不计)
(1)求电场强度的大小;
(2)求感光板到x轴的距离;
(3)磁感应强度为多大时所有粒子均能打到板上?并求出此时ab板上被
粒子打中的区域的长度。![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241331051075579.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133104764310.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133104764310.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133104873696.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133104764310.png)
(1)求电场强度的大小;
(2)求感光板到x轴的距离;
(3)磁感应强度为多大时所有粒子均能打到板上?并求出此时ab板上被
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133104764310.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241331051075579.png)
(1)
(2)
(3) ![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133105216943.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133105138789.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133105169731.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133105216943.png)
(1)根据动能定理:
------ (2分)
由于
可得: 场强大小为
------ (1分)
(2)对于沿x轴负方向射出的粒子进入磁场时与x轴负方向夹角
------ (1分)
其在电场中沿x方向的位移
------ (2分)
易知若此粒子不能打到ab板上,则所有粒子均不能打到ab板,因此此粒子轨迹必与ab板相切 ------ (2分)
根据洛伦兹力提供向心力
------(1分)
可得其圆周运动的半径![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133105606169.png)
------ (2分)
------ (1分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241331057317029.png)
(3)易知沿x轴正方向射出的粒子若能打到ab板上,则所有粒子均能打到板上。其临界情况就是此粒子轨迹恰好与ab板相切。可知此时
------ (1分)
------ (1分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241331058717020.png)
磁感应强度为原来的
,即当
恰好所有粒子均能打到板上 ------ (1分)
ab板上被打中区域的长度
------ (3分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133105263987.png)
由于
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133105325488.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133105138789.png)
(2)对于沿x轴负方向射出的粒子进入磁场时与x轴负方向夹角
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133105403525.png)
其在电场中沿x方向的位移
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241331054811457.png)
易知若此粒子不能打到ab板上,则所有粒子均不能打到ab板,因此此粒子轨迹必与ab板相切 ------ (2分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133105512702.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133105559723.png)
可得其圆周运动的半径
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133105606169.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133105637467.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133105169731.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241331057317029.png)
(3)易知沿x轴正方向射出的粒子若能打到ab板上,则所有粒子均能打到板上。其临界情况就是此粒子轨迹恰好与ab板相切。可知此时
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133105778893.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133105824583.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241331058717020.png)
磁感应强度为原来的
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133105902327.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133105980738.png)
ab板上被打中区域的长度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133105216943.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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