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笔者对一道有关有效值求解的考题提供的命题考查意图持有疑义,随对此试题及解析通过质疑一一特例验证一一数学推理等过程验证笔者观点,借此抛砖引玉,以期同仁共同探讨。[原题]如图1所示,光滑长导体轨道PQ、MT固定在水平面上,左端连接电阻R=1Ω,以M点为坐标原点,MN为x轴、MP为y轴建立坐标系,则PQ轨道的方程为y=1.5+0.5sin20πx(m)。现紧靠MP垂直于MN放置一根光滑导体杆,长度为l=2m,质量m=0.2kg,整个装置处于方向竖直向下、大小B=1T的匀强磁场中。在t=0时刻开始在水平向右的拉力F作用下以速度v=1m/s从MP位置处开始向右匀速运动,运动过程中杆与导轨保持良好接触,除R外其他电阻不计。求:电流的有效值I。
The author tries to hold a doubt about the proposition examination question that is provided for a valid value-solving question. With verification of this question and parsing through questioning, one-to-one exception verification and one-by-one mathematical reasoning, the author tries to verify the author’s point of view and thereby to initiate a discussion with my colleagues. [Original title] As shown in Figure 1, the smooth long conductor tracks PQ and MT are fixed on the horizontal plane. The left end is connected with a resistance of R=1 Ω. The M point is used as the origin of the coordinates. The MN is the x axis and the MP is the y axis to establish the coordinate system. The equation for the PQ orbit is y=1.5+0.5sin20πx(m). A smooth conductor bar is placed next to the MP perpendicular to the MN. The length is l=2 m, and the mass m is 0.2 kg. The entire device is in a uniform magnetic field with a downward vertical direction and a size of B=1T. At t=0, the horizontal rightward pulling force F starts to move from the MP position to the right at the speed v=1m/s, and the rod and the guide rail maintain a good contact during the movement, and the resistance other than R is not counted. Find: The effective value of the current I.