题目

一个质量m=0.1g的小滑块，带有q=5×10﹣4C的电荷，放置在倾角α=30°的光滑斜面上（斜面绝缘），斜面置于B=0.5T的匀强磁场中，磁场方向垂直纸面向里，如图所示．小滑块由静止开始沿斜面下滑，其斜面足够长，小滑块滑至某一位置时，要离开斜面．问：                                                                        （1）小滑块带何种电荷？                                                                        （2）小滑块离开斜面时的瞬时速度多大？                                               （3）该斜面的长度至少多长？                                                                                                                                              答案：解：（1）由题意可知：小滑块受到的洛伦兹力垂直斜面向上．                       小滑块滑至某一位置时，要离开斜面，根据左手定则可得：小滑块带负电．                                               （2）由题意：当滑块离开斜面时，洛伦兹力：Bqv=mgcosα，                         则=m/s．                       （3）又因为离开之前，一直做匀加速直线运动，                                            则有：mgsinα=ma，                                                                            即a=gsinα=5m/s2，                                                                             由v2=2ax得： m                                  答：（1）小滑块带负电荷；                                                                    （2）小滑块离开斜面时的瞬时速度是m/s；                                             （3）该斜面的长度至少长1.2m．                                                            　                                                                                                      

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