题目内容
（分）平面直角坐标系xOy中，第1象限存在沿y轴负方向的匀强电场，第Ⅳ象限存在垂直于坐标平面向外的匀强磁场，磁感应强度大小为B。一质量为m、电荷量为q的带正电的粒子从y轴正半轴上的M点以速度v0垂直于y轴射入电场，经x轴上的N点与x轴正方向成60°角射入磁场，最后从y轴负半轴上的P点与y轴正方向成600角射出磁场，如图所示。不计粒子重力，求
（1）粒子在磁场中运动的轨道半径R；
（2）粒子从M点运动到P点的总时间t；
（3）匀强电场的场强大小E。
（1） 
（2） 
（3） 
解析:
（1）设粒子过N点时的速度为v，根据平抛运动的速度关系
v＝··························································· ①
分别过N、P点作速度方向的垂线，相交于Q点，则Q是粒子在磁场中做匀速圆周运动的圆心，根据牛顿第二定律 qvB＝··································································· ···· ②
联立①②解得轨道半径 R＝ ····························· ③
（2）设粒子在电场中运动的时间为t1，有 ON＝v0t1 ····················································· ④
由几何关系得 ON＝Rsin30°＋Rcos30°········································································ ⑤
联立③④⑤解得 t1＝··················································································· ⑥
粒子在磁场中做匀速圆周运动的周期 T＝ ····························································· ⑦
由几何关系知∠NQP＝150°，设粒子在磁场中运动的时间为t2 t2＝T····························· ⑧
联立⑦⑧解得 t2＝···························································································· ⑨
故粒子从M点运动到P点的总时间 t＝t1＋t2＝(1＋＋)··········································· ⑩
（3）粒子在电场中做类平抛运动，设加速度为a qE=ma ··············································· ⑾
设沿电场方向的分速度为vy vy=at1 ········································································ ⑿
又 vy=v0tan600 ··································································································· ⒀
联立⑥⑾⑿⒀解得 E＝··············································································· ⒁
（08年天津卷）(16分)在平面直角坐标系xOy中，第1象限存在沿y轴负方向的匀强电场，第Ⅳ象限存在垂直于坐标平面向外的匀强磁场，磁感应强度为B。一质量为m、电荷量为q的带正电的粒子从y轴正半轴上的M点以速度v0垂直于Y轴射入电场，经x轴上的N点与x轴正方向成θ=60°角射入磁场，最后从y轴负半轴上的P点垂直于Y轴射出磁场，如图所示。不计粒子重力，求
（08年天津卷）23．(16分)在平面直角坐标系xOy中，第1象限存在沿y轴负方向的匀强电场，第Ⅳ象限存在垂直于坐标平面向外的匀强磁场，磁感应强度为B。一质量为m、电荷量为q的带正电的粒子从y轴正半轴上的M点以速度v0垂直于Y轴射入电场，经x轴上的N点与x轴正方向成θ=60°角射入磁场，最后从y轴负半轴上的P点垂直于Y轴射出磁场，如图所示。不计粒子重力，求
存在垂直于坐标平面向外的匀强磁场，磁感应强度为B.一质量为m、电荷量为q的带正电的粒子从y轴正半轴上的M点以速度v0垂直于y轴射入电场，经x轴上的N点与x轴正方向成θ=60°角射入磁场，最
后从y轴负半轴上的P点垂直于y轴射出磁场，如图所示，不计粒子重力，求
（2）粒子在磁场中运动的轨道半径r；
（2）粒子在磁场中运动的轨道半径r；