题目内容
(22分)如图甲所示,水平直线MN下方有竖直向上的匀强电场,现将一重力不计、荷质比
的正电荷置于电场中的O点由静止释放,经过
×10—5s时间以后电荷以v0=1.5×l04m/s的速度通过MN进入其上方的匀强磁场,磁场方向与纸面垂直,磁感应强度B按图乙所示规律周期性变化(图乙中磁场以垂直纸面向外为正.以电荷第一次通过MN时为t=0时刻).不考虑磁场变化产生的电场.
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/2014082500403867216650.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250040387033270.png)
求:⑴.匀强电场的电场强度E;
⑵.
×10-5s时刻电荷与O点的水平距离;
⑶.如果在O点正右方d= 68cm处有一垂直于MN的足够大的挡板,求电荷从O点出发运动到挡板的时间.
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004038625893.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004038656427.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/2014082500403867216650.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250040387033270.png)
求:⑴.匀强电场的电场强度E;
⑵.
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004038719554.png)
⑶.如果在O点正右方d= 68cm处有一垂直于MN的足够大的挡板,求电荷从O点出发运动到挡板的时间.
(1)
(2)
(3) ![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004038797803.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250040387501268.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004038765915.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004038797803.png)
试题分析:(1)电荷在电场中做匀加速直线运动,设其在电场中运动的时间为t1,有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004038812495.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004038843585.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250040387501268.png)
(2)当磁场垂直纸面向外时,由
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004038875761.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004038890922.png)
周期
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250040389061138.png)
当磁场垂直纸面向里时,电荷运动的半径:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004038937969.png)
周期
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250040389531151.png)
故电荷从t=0时刻开始做周期性运动,其运动轨迹如图所示.
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/2014082500403898427752.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004038999758.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004038765915.png)
(3)电荷从第一次通过MN开始,其运动的周期为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004039046769.png)
根据电荷的运动情况可知,电荷到达档板前运动的完整周期数为15个,有:
电荷沿ON运动的距离:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004039062797.png)
故最后8cm的距离如图所示,
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/2014082500403907715132.png)
有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004039093763.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004039124590.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004039140498.png)
故电荷运动的总时间:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250040391551497.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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