Question

如圖所示，單匝線圈ABCD在外力作用下以速度v向右勻速進入勻強磁場，第二次又以速度2v勻速進入同一勻強磁場．求：

（1）第二次與第一次線圈中最大電流之比；

（2）第二次與第一次外力做功的最大功率之比；

（3）第二次與第一次線圈中產(chǎn)生熱量之比．

Answer 1

（1）2∶1  （2）4∶1（3）2∶1  

解析:

（1）線圈以速度v勻速進入磁場，當CD邊在磁場中時，線框中感應電動勢其中L為CD邊的長度．                                             

   此時線框中的感應電流為，其中R為線框的總電阻．   

   同理，線圈以速度2v勻速進入磁場時，線框中的感應電流最大值為

   所以第二次與第一次線圈中最大電流之比為2∶1                      （4分）

  （2）線圈以速度v勻速進入磁場，當CD邊在磁場中時，CD邊受安培力最大，最大值為 ．由于線圈做勻速運動，所以此時外力也最大，且外力大小等于安培力大小，此時外力的功率為．                 

   同理，線圈以速度2v勻速進入磁場時，外力的最大功率為．

所以第二次與第一次外力做功的最大功率之比為4∶1                    （4分）

  （3）線圈以速度v勻速進入磁場，線框中的感應電流為

   設AD邊長為l，則線框經(jīng)過時間完全進入磁場，此后線框中不再有感應電流．所以第一次線框中產(chǎn)生的熱量為         

同理，線圈以速度2v勻速進入磁場時，線框中產(chǎn)生的熱量為                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    

所以第二次與第一次線圈中產(chǎn)生熱量之比為2∶1                        （4分）