如图所示,单匝线圈ABCD在外力作用下以速度v向右匀速进入匀强磁场,第二次又以速度2v匀速进入同一匀强磁场.求:(1)第二次与第一次线圈中最大电流之比;(2)第

如图所示,单匝线圈ABCD在外力作用下以速度v向右匀速进入匀强磁场,第二次又以速度2v匀速进入同一匀强磁场.求:(1)第二次与第一次线圈中最大电流之比;(2)第

题型:不详难度:来源:
如图所示,单匝线圈ABCD在外力作用下以速度v向右匀速进入匀强磁场,第二次又以速度2v匀速进入同一匀强磁场.求:

(1)第二次与第一次线圈中最大电流之比;
(2)第二次与第一次外力做功的最大功率之比;
(3)第二次与第一次线圈中产生热量之比.
答案
(1)2∶1 (2)4∶1(3)2∶1  
解析
(1)线圈以速度v匀速进入磁场,当CD边在磁场中时,线框中感应电动势其中L为CD边的长度.                                            
此时线框中的感应电流为,其中R为线框的总电阻.   
同理,线圈以速度2v匀速进入磁场时,线框中的感应电流最大值为
所以第二次与第一次线圈中最大电流之比为2∶1                     (4分)
(2)线圈以速度v匀速进入磁场,当CD边在磁场中时,CD边受安培力最大,最大值为 .由于线圈做匀速运动,所以此时外力也最大,且外力大小等于安培力大小,此时外力的功率为.                 
同理,线圈以速度2v匀速进入磁场时,外力的最大功率为
所以第二次与第一次外力做功的最大功率之比为4∶1                   (4分)
(3)线圈以速度v匀速进入磁场,线框中的感应电流为
设AD边长为l则线框经过时间完全进入磁场,此后线框中不再有感应电流.所以第一次线框中产生的热量为         
同理,线圈以速度2v匀速进入磁场时,线框中产生的热量为                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   
所以第二次与第一次线圈中产生热量之比为2∶1                       (4分)           
举一反三
如图所示,在光滑的水平面上,有一垂直向下的匀强磁场分布在宽为L的区域内,有一个边长为aa<L的正方形闭合线圈以初速v0垂直磁场边界滑过磁场后速度变为vv<v0那么[]

A.完全进入磁场中时线圈的速度大于v0+v/2;
B.安全进入磁场中时线圈的速度等于v0+v/2
C.完全进入磁场中时线圈的速度小于v0+v/2
D.以上情况A、B均有可能,而C是不可能的
(提示在时间△t内安培力的冲量
题型:不详难度:| 查看答案

(1)金属棒ab的最大速度;
(2)金属棒ab运动达到稳定状态后,1s钟内回路产生的焦耳热。
题型:不详难度:| 查看答案

求⑴线框进入磁场过程中安培力做的功是多少?
⑵线框穿出磁场过程中通过线框任一截面的电荷量q是多少?  

题型:不详难度:| 查看答案

①ab导体棒运动的最大速度。
②ab导体棒匀速运动时重力的功率、与整个回路的电功率是否等大?通过计算说明。
③为使导体棒cd静止,物体M的最小质量为多大?
题型:不详难度:| 查看答案


存在匀强磁场.磁场方向垂直于轨道平面向上,磁感应强度为B.P、M间所接阻值为R的
电阻.质量为m的金属杆ab水平放置在轨道上,其有效电
阻为r.现从静止释放ab,当它沿轨道下滑距离s时,达到
最大速度.若轨道足够长且电阻不计,重力加速度为g.
求:
(1)金属杆ab运动的最大速度;
(2)金属秆ab运动的加速度为gsin时,电阻R上的电功率;
(3)金属杆ab从静止到具有最大速度的过程中,克服安培力所做的功
题型:不详难度:| 查看答案
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