题目内容
⑵如果粒子经纸面内Q点从磁场中射出,出射方向与半圆在Q点切线方向的夹角为φ(如图)。求入射粒子的速度。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241154020691132.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241154021941021.gif)
⑴由于粒子在P点垂直射入磁场,故圆弧轨道的圆心在AP上,AP是直径。
设入射粒子的速度为v1,由洛伦兹力的表达式和牛顿第二定律得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115402303610.gif)
解得:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115402350525.gif)
⑵设O/是粒子在磁场中圆弧轨道的圆心,连接O/Q,设O/Q=R/。
由几何关系得:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115402412493.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115402428501.gif)
由余弦定理得:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115402475785.gif)
解得:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115402506930.gif)
设入射粒子的速度为v,由![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115402521541.gif)
解出:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241154021941021.gif)
设入射粒子的速度为v1,由洛伦兹力的表达式和牛顿第二定律得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241154022871564.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115402303610.gif)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115402350525.gif)
⑵设O/是粒子在磁场中圆弧轨道的圆心,连接O/Q,设O/Q=R/。
由几何关系得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115402412493.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115402428501.gif)
由余弦定理得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115402475785.gif)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115402506930.gif)
设入射粒子的速度为v,由
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115402521541.gif)
解出:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241154021941021.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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