题目内容
如图所示,M、N为两平行金属板相距d="0.4" m,板间有垂直纸面的匀强磁场B="0.25" T。图中I和Ⅱ是两根与M、N平行的金属导轨,I与M相距
、Ⅱ与N相距
,I与Ⅱ之间接一电阻R="0." 3Ω。现有一金属杆在上述装置上(接触良好)向右水平运动,已知金属杆ab间电阻
="0." 2Ω,若有一个带电量
C的粒子以
="7" m/s沿水平向右射入MN间,恰好能匀速运动。求:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241142515022588.jpg)
(1)两极间电势差
。
(2)ab杆运动速度。
(3)为保持ab杆匀速运动,所需外力F。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114251377234.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114251377234.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114251408326.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114251424523.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114251439206.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241142515022588.jpg)
(1)两极间电势差
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114251580364.gif)
(2)ab杆运动速度。
(3)为保持ab杆匀速运动,所需外力F。
(1)0.7 V
(2)8m/s
(3)0. 05 N。
(2)8m/s
(3)0. 05 N。
(1)依题意带电拉子做匀速直线运动,故必有粒子所受洛伦兹力与拉子在平行板间电场力相平衡,即![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114251595669.gif)
V="0.7" V
(2)设金属杆运动速度为v,其中ac和db部分产生感应电动势都为
,由于
,故cd部分感应电动势为![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114251689935.gif)
得
="0." 2 V
又![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114251829482.gif)
故
8m/s
(3)由于金属杆匀速运动,所以外力
与杆上安培力
相等。即
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114252188953.gif)
又因为
1 A
解得
=0. 05 N。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114251595669.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114251611735.gif)
(2)设金属杆运动速度为v,其中ac和db部分产生感应电动势都为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114251642213.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114251658531.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114251689935.gif)
得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114251642213.gif)
又
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114251829482.gif)
故
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114251939490.gif)
(3)由于金属杆匀速运动,所以外力
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114251954334.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114251985227.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114252188953.gif)
又因为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114252204597.gif)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114251954334.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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