题目内容
如图所示,一个半径为r的半圆形线圈,以直径ab为轴匀速转动,转速为n,ab的左侧有垂直于纸面向里(与ab垂直)的匀强磁场,磁感应强度为B。 M和N是两个集流环,负载电阻为R,线圈、电流表和连接导线的电阻不计。求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241333136822875.png)
(1)感应电动势的最大值;]
(2)从图示位置起转过1/4转的时间内通过负载电阻R的电荷量;
(3)电流表的示数.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241333136822875.png)
(1)感应电动势的最大值;]
(2)从图示位置起转过1/4转的时间内通过负载电阻R的电荷量;
(3)电流表的示数.
(1) π2Bnr2. (2)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133313776946.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133313729629.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133313776946.png)
(1)线圈绕轴匀速转动时,在电路中产生如图所示的交变电流.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241333138381719.png)
此交变电动势的最大值为Em=BSω=B·
·2πn=π2Bnr2. 3分
(2)在线圈从图示位置转过1/4转的时间内,电动势的平均值为![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133314041659.png)
通过R的电荷量
. 4分
(3)设此交变电动势在一个周期内的有效值为E′,由有效值的定义得
解得
. 3分
故电流表的示数为
2分
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241333138381719.png)
此交变电动势的最大值为Em=BSω=B·
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133314010492.png)
(2)在线圈从图示位置转过1/4转的时间内,电动势的平均值为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133314041659.png)
通过R的电荷量
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241333140881369.png)
(3)设此交变电动势在一个周期内的有效值为E′,由有效值的定义得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241333141191147.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133314150610.png)
故电流表的示数为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133313776946.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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