如图甲所示,左侧发电装置由一个留有小缺口的圆形线圈和能产生辐向磁场的磁体组成,辐向磁场分布关于线圈中心竖直轴对称,线圈所在处磁感应强度大小均为。线圈半径r,电阻不计,缺口处通过足够长轻质软导线与间距
的水平平行光滑金属轨道
相连,轨道间接有电容为
的电容器,
区域内有竖直向下,的匀强磁场
,紧靠
处有一根质量m,电阻R的金属杆a。绝缘轨道
区域内有方向竖直向下,大小随x轴(
为坐标原点,向右为正方向)变化的磁场,变化规律满足
,同一位置垂直轨道方向磁场相同,紧靠
处放置质量为m、电阻为
的“
”形金属框EFGH,FG边长度为L,EF边长度为
。
时刻单刀双掷开关S和接线柱1接通,圆形线圈在外力作用下沿竖直方向运动,其速度按照图乙规律变化,取竖直向上为速度正方向。
时将S从1拨到2,同时让金属杆a以初速度
在磁场中向右运动,金属杆a达到稳定速度
后在
处与金属框EFGH发生完全非弹性碰撞组合成一闭合的长方形金属框。不考虑电流产生的磁场影响,除已给电阻其它电阻不计。求(结果可用r、m、
、
、
、k中的字母表):
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecb7de5df21b8271f5a57ae223971175.png)
(2)a杆到达
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b6bbd5a2588d7b943222844bb73d20b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f44c235d8b49207ad3f2d77dc5d6cf20.png)
(3)金属杆a与“”形金属框发生完全非弹性碰撞组合成一闭合的长方形金属框,金属框最终静止时HE边所在位置的x轴坐标。
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