In this paper, we discuss four errors introductory physics students make when attempting to add two inverse-square law vectors. We observe multiple instances in which students (1) add vectors as if they were scalars, (2) project the r (or r ²) in the denominator, instead of the entire vector, when attempting to find the vector’s components, (3) incorrectly apply the Pythagorean theorem when attempting to calculate the magnitude of the resultant vector, and (4) incorrectly relate the signs of the components of an electric field (or force) to the signs of the electric charges. While these are not the only errors students make, they are the most frequently occurring based on our analysis of 678 exams taken by students in either introductory mechanics or electricity and magnetism (E&M). We then show how these errors can be encoded into a new type of activity or assessment question which we call a ‘student error task.’ Introductory physics instructors can use the student error task in this paper as a way to engage or assess their students’ understandings of how to add two inverse-square law vectors.

中文翻译：

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学生在使用平方反比定律向量时犯的四个错误

在本文中，我们讨论了物理学入门学生在尝试将两个平方反比定律向量相加时犯的四个错误。我们观察到多个实例，其中学生（1）将向量添加为标量，（2）投影r（或者r ²）当试图找到向量的分量时，在分母中而不是整个向量中，（3）在尝试计算结果向量的大小时错误地应用毕达哥拉斯定理，以及（4）错误地关联分量的符号电场（或力）的符号。虽然这些并不是学生犯的唯一错误，但根据我们对机械学入门或电学和磁学 (E&M) 学生参加的 678 次考试的分析，这些错误是最常发生的。然后，我们展示如何将这些错误编码成一种新类型的活动或评估问题，我们称之为“学生错误任务”。物理入门教师可以使用本文中的学生错误任务来吸引或评估学生对如何添加两个平方反比定律向量的理解。