问题 计算题

(12分)两足够长的平行光滑金属导轨,问距为L倾斜放置,与水平面的夹角为,处于磁感应强度为B方向垂直于导轨平面的匀强磁场中.一质量为m、长为L、电阻为R1的导体棒ab放在导轨上,与导轨垂直且接触良好,不计导轨电阻.

(1)如图甲,导轨上端接一个内阻为r的直流电源,导体棒能恰好静止,求电源的电动势.

(2)如图乙,导轨上端接一个阻值为R:的定值电阻,让导体棒由静止开始下滑.加速过程中的速度为v时,导体棒的加速度是多少?

答案

(1)(2)

题目分析:(1) 回路中的电流为 

导体棒受到的安培力为 

对导体棒受力分析知 

联立上面三式解得: 

(2)当ab杆速度为v时,感应电动势E=BLv,此时电路中电流 (1分)

导体棒ab受到安培力 

根据牛顿运动定律,有

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