题目

I was working as a consultant in a beer company, helping the president and senior vice-presidents form and carry out their new planning projects. It was really a great challenge. At the same time, my mother was in the final stages of cancer. I worked during the day and drove 40 miles home to be with her every night. It was tiring and stressful, but it was what I wanted to do. My commitment was to continue to do excellent consulting during the day, even though my evenings were very hard. I didn’t want to bother the president with my situation, yet I felt someone at the company needed t如图所示，电离室中存在大量密度相同、大小不同的球状纳米粒子，它们在电离室电离后均带正电，且所带电量与其表面积成正比。电离后的纳米粒子缓慢地通过小孔O1进入板间电压为U的电场加速后，又从小孔O2沿水平方向射入右方匀强磁场区域。已知匀强磁场区域I Ⅱ的水平宽度均为d，竖直方向足够长，磁感应强度大小均为B，方向分别垂直纸面向里和向外。设这些纳米粒子的最小半径为r0，其他粒子半径均为r0的整数倍，且半径最小的纳米粒子质量为m0、带电量为q0，不计纳米粒子的重力。已知球表面积公式S=4πr2，球体积公式．求；(1)半径为r0和2r0的纳米粒子经电场加速后速度之比；(2)要使所有的纳米粒子均能穿过磁场区域，确定加速电压U应满足何条件；(3)若加速电压取U0时，半径为r0的粒子恰好不能穿过磁场区域。求出这种情况下，半径为2r0的纳米粒子先后穿过磁场区域I和Ⅱ经历的总时间t。