Question

如圖，勻強(qiáng)電場(chǎng)中有一半徑為r的光滑絕緣圓軌道，軌道平面與電場(chǎng)方向平行．a(chǎn)、b為軌道直徑的兩端，該直徑與電場(chǎng)方向平行．一電荷量為q（q＞0）的質(zhì)點(diǎn)沿軌道內(nèi)側(cè)運(yùn)動(dòng)，經(jīng)過(guò)a點(diǎn)和b點(diǎn)時(shí)對(duì)軌道壓力的大小分別為N_a和N_b．不計(jì)重力，求：（1）電場(chǎng)強(qiáng)度的大小E；                                                                                    

（2）質(zhì)點(diǎn)經(jīng)過(guò)a點(diǎn)和b點(diǎn)時(shí)的動(dòng)能．                                                                  

                                                                                        

                                                                                                                           

Answer 1

       解：質(zhì)點(diǎn)所受電場(chǎng)力的大小為f=qE ①

設(shè)質(zhì)點(diǎn)質(zhì)量為m，經(jīng)過(guò)a點(diǎn)和b點(diǎn)時(shí)的速度大小分別為v_a和v_b，由牛頓第二定律有：

 ②

 ③

設(shè)質(zhì)點(diǎn)經(jīng)過(guò)a點(diǎn)和b點(diǎn)時(shí)的動(dòng)能分別為E_ka和E_kb，有：

E_ka=mv_a² ④

E_kb=mv_b² ⑤

根據(jù)動(dòng)能定理有：E_kb﹣E_ka=2rf⑥

聯(lián)立①②③④⑤⑥式得：

答：：（1）電場(chǎng)強(qiáng)度的大小E為（N_b﹣N_a）；

（2）質(zhì)點(diǎn)經(jīng)過(guò)a點(diǎn)和b點(diǎn)時(shí)的動(dòng)能分別為：（N_b+5N_a）和（5N_b+N_a）．