问题 计算题

如图所示,在y轴的右侧存在磁感应强度为B的方向垂直纸面向外的匀强磁场,在x轴的上方有一平行板式加速电场。有一薄绝缘板放置在y轴处,且与纸面垂直。现有一质量为m、电荷量为q的粒子由静止经过加速电压为U的电场加速,然后以垂直于板的方向沿直线从A处穿过绝缘板,而后从x轴上的D处以与x轴负向夹角为30°的方向进入第四象限,若在此时再施加一个电场可以使粒子沿直线到达y轴上的C点(C点在图上未标出)。已知OD长为l,不计粒子的重力。求:

(1)粒子射入绝缘板之前的速度;

(2)粒子经过绝缘板时损失了多少动能;

(3)所加电场的电场强度和带电粒子在y周的右侧运行的总时间。

答案

解:(1)粒子在电场中加速由动能定理可知

解得

(2)粒子在磁场中作圆周运动轨迹如图

由几何关系可得轨道半径为2l

解得=

由动能定理得

代入数据解得

所以损失动能为

或者,带入结果得

(3)粒子若作直线运动则=Eq

代入数据解得E=,方向与x轴正向斜向下成60°角

粒子在第一象限作匀速圆周运动的时间t1=

粒子在第四象限做匀速直线运动时间t2==

粒子x轴右侧运行的总时间t==

完形填空
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