Writing Position Vectors in 3-d Space: A Student Difficulty With Spherical Unit Vectors in Intermediate E&M

An intermediate E&M course (i.e. based on Griffiths 1) involves the extensive integration of vector calculus concepts and notation with abstract physics concepts like field and potential. We hope that students take what they have learned in their math courses and apply it to help represent and make sense of the physics. To assess how well students are able to do this integration and application I have developed several simple concept tests on position and unit vectors in non-Cartesian coordinate systems as they are used in intermediate E&M. In this paper I describe one of these concept tests and present results that show both undergraduate physics majors and physics graduate students have difficulty using spherical unit vectors to write position vectors in 3-d space.