Question

圖1所示,y軸右側(cè)有垂直紙面向里的勻強(qiáng)磁場(chǎng),第Ⅱ象限內(nèi)有水平的勻強(qiáng)電場(chǎng).有一質(zhì)量為m、電荷量為q的帶負(fù)電的粒子(不計(jì)重力),從P點(diǎn)以初速度v₀沿+y方向射入電場(chǎng)中,OP=L,粒子在電場(chǎng)中運(yùn)動(dòng)一段時(shí)間后進(jìn)入磁場(chǎng),進(jìn)入磁場(chǎng)時(shí),速度方向與+x方向成30°角,并且恰好經(jīng)過坐標(biāo)原點(diǎn)O再進(jìn)入電場(chǎng)中繼續(xù)運(yùn)動(dòng).求:?
(1)電場(chǎng)強(qiáng)度E的大小;?
(2)磁感應(yīng)強(qiáng)度B的大小.?

圖1

Answer 1

(1)粒子在電場(chǎng)中運(yùn)動(dòng),沿y方向的位移y=v₀t                        ①
速度v_y=v₀                                                                                                                                                                     ②
沿x方向的位移為                         ③
速度                                       ④?
由題意知                                     ⑤
由②⑤得                                     ⑥?
由③④⑥得                                       ⑦
                                              ⑧
(2)由①⑦兩式得出進(jìn)入磁場(chǎng)時(shí)的位置距O點(diǎn)的距離     ⑨
設(shè)在磁場(chǎng)中做圓周運(yùn)動(dòng)的半徑為R,則有Rcos30°=y/2                  ⑩?
又由于qBv=mv²/R                                                                      11
                                                               12