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利用柯西不等式在中学物理解题中往往可以巧妙地解决一些较难的极值问题,比如可以证明,两段导线的长度、材料和质量均相同,粗细均匀的导线电阻比粗细不均匀的导线电阻小,由此可知,粗细均匀乃是衡量导线质量好坏的标准之一。那么对于长度相等,材料相同,但质量不等的导线,粗细均匀与否,又会有怎样的极值问题呢?笔者就2016年鸟鲁木齐地区高三年级第二次物理诊断性高考试题中一道磁场中“落线圈”问题展开讨论,揭示考生应注重提升运用数学知识解决物理问题的能力。
Cauchy inequality is often used to solve some difficult extremum problems in middle school physics problem solving. For example, it can be proved that the lengths, materials and qualities of two wires are the same. The wire with uniform thickness and thickness has a higher resistance than the wires with uneven thickness Resistance is small, we can see that even the thickness of the wire is one of the criteria to measure the quality of good or bad. So for the same length, the same material, but the quality of the wire, the thickness is uniform or not, what will be the extreme value of the problem? I author in 2016 in Luxiqi third grade senior high school physician diagnostic test A discussion of the problem of “falling coil” in a magnetic field reveals that candidates should focus on improving the ability of using mathematical knowledge to solve physical problems.