题目内容
如图所示,固定在水平桌面上平行光滑金属导轨cd、eg之间的距离为L,d、e两点接一个阻值为R的定值电阻,整个装置处于方向竖直向下的匀强磁场中(磁场范围足够大)。有一垂直放在导轨上的金属杆ab,其质量为m、电阻值为r0在平行导轨的水平拉力F的作用下做初速度为零的匀加速直线运动,F随时间t变化规律为F=F0+kt,其中F0和k为已知的常量,经过t0时间撤去拉力F.轨道的电阻不计。求
(1)t0时金属杆速度的大小v0;
(2)磁感应强度的大小B;
(3)t0之后金属杆ab运动速度大小v随位移大小x变化满足:
,试求撤去拉力F到金属杆静止时通过电阻R的电荷量q。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241323275745144.jpg)
(1)t0时金属杆速度的大小v0;
(2)磁感应强度的大小B;
(3)t0之后金属杆ab运动速度大小v随位移大小x变化满足:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241323276051061.png)
(1)
(2)
(3) ![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241323277301147.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132327652830.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241323276981116.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241323277301147.png)
(1)金属杆的加速度大小为
,
时刻速度大小为
,电流为
,则
①(2分)
②(2分)
③(1分)
由①②③得
④(1分)
由于
是恒量,所以必须
⑤(1分)
即
⑥(2分)
⑦(2分)
(2)由⑤得
⑧(2分)
把⑥代入得
⑨(2分)
(3)金属杆从撤去拉力F到静止时通过的距离
满足
得
⑩ (1分)
通过电阻
的电荷量
11 (1分)
其中
12 (1分)
由⑩1112式得
13(1分)
将⑦⑨代入得
14 (1分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132327823283.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132327854267.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132327886265.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132327948251.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132327979859.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132328010690.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132328073420.png)
由①②③得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241323281201196.png)
由于
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132327823283.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132328260863.png)
即
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132328291610.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132327652830.png)
(2)由⑤得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132328400947.png)
把⑥代入得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241323276981116.png)
(3)金属杆从撤去拉力F到静止时通过的距离
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132328494266.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241323285561100.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132328619998.png)
通过电阻
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132328681303.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132328712893.png)
其中
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132328775741.png)
由⑩1112式得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132328822708.png)
将⑦⑨代入得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241323277301147.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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