Question

（12分）如圖所示，單匝線圈ABCD在外力作用下以速度v向右勻速進(jìn)入勻強(qiáng)磁場(chǎng)，第二次又以速度2v勻速進(jìn)入同一勻強(qiáng)磁場(chǎng)．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

（12分）

（1）線圈以速度v勻速進(jìn)入磁場(chǎng)，當(dāng)CD邊在磁場(chǎng)中時(shí)，線框中感應(yīng)電動(dòng)勢(shì)其中L為CD邊的長(zhǎng)度．                                            

   此時(shí)線框中的感應(yīng)電流為，其中R為線框的總電阻．   

   同理，線圈以速度2v勻速進(jìn)入磁場(chǎng)時(shí)，線框中的感應(yīng)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(jìn)入磁場(chǎng)，當(dāng)CD邊在磁場(chǎng)中時(shí)，CD邊受安培力最大，最大值為 ．由于線圈做勻速運(yùn)動(dòng)，所以此時(shí)外力也最大，且外力大小等于安培力大小，此時(shí)外力的功率為．                 

   同理，線圈以速度2v勻速進(jìn)入磁場(chǎng)時(shí)，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(jìn)入磁場(chǎng)，線框中的感應(yīng)電流為

   設(shè)AD邊長(zhǎng)為l，則線框經(jīng)過(guò)時(shí)間完全進(jìn)入磁場(chǎng)，此后線框中不再有感應(yīng)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(jìn)入磁場(chǎng)時(shí)，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）