Question

图1所示,y轴右侧有垂直纸面向里的匀强磁场,第Ⅱ象限内有水平的匀强电场.有一质量为m、电荷量为q的带负电的粒子(不计重力),从P点以初速度v₀沿+y方向射入电场中,OP=L,粒子在电场中运动一段时间后进入磁场,进入磁场时,速度方向与+x方向成30°角,并且恰好经过坐标原点O再进入电场中继续运动.求:?
(1)电场强度E的大小;?
(2)磁感应强度B的大小.?

图1

Answer 1

(1)粒子在电场中运动,沿y方向的位移y=v₀t                        ①
速度v_y=v₀                                                                                                                                                                     ②
沿x方向的位移为                         ③
速度                                       ④?
由题意知                                     ⑤
由②⑤得                                     ⑥?
由③④⑥得                                       ⑦
                                              ⑧
(2)由①⑦两式得出进入磁场时的位置距O点的距离     ⑨
设在磁场中做圆周运动的半径为R,则有Rcos30°=y/2                  ⑩?
又由于qBv=mv²/R                                                                      11
                                                               12