t=n()(n=2，4，6…)                                                                                 (2分)

x=                                                                               (2分)

当n为偶数时，则有

x=n(2r₁-2r₂)(n=2，4，6…)                                                                                       (2分)

用t表示从开始到此时的时间，

当n为奇数时，则有

t₁=                                                                                                   (2分)

(2)设用x表示至第n次过x轴的整个过程中，粒子沿x轴方向的位移大小，当n为奇数时则有

x₁=2r₁=                                                                                                    (2分)

粒子第一次过x轴时的经历的时间为

              T₂=

粒子第一次过x轴时的坐标为

              T₁=

        r₂=

  可得，r₁=

  由qvB=                                                                               (2分)

47.解：(1)设带电粒子的电量为q，质量为m，在B₁和B₂中运动轨道半径分别为r₁和r₂，周期分别为T₁和T₂，