Sometimes students can just set up the integral and leave it that way.
Other times they have to solve it. But this is not a random choice
depending on how I feel when I write the exam. There are definite times one
is more appropriate than another. I'll give two examples.
(1) The student is setting up an integral to evaluate the electric field at
a point caused by some known charge distribution. (This is not a Gauss' Law
method, but an infinite sum over continuous charges.) In this situation the
conceptual part the students need to learn is setting up the integral. Once
the integral is set up, integrating it is not physics anymore, it's just
math. I myself will often run to an integral table if I end up with an
integral I don't recognize, or if I am just too lazy to figure it out.
(2) The student is trying to learn the concept of how a line integral or how
a surface integral works. In this situation, understanding what a
line/surface integral is and how it works is vital for the physicist, even
though it is just math. Three points here... (a) students may have never
done this in calculus class, so we have to teach the whole thing, (b) the
concept of a surface or line vector and how that relates to the
electric/magnetic field is an important concept, (c) the concept of looking
at symmetry and seeing how the surface/line integral simplifies and can
easily be solved in some cases, yet turn into a real mess in other cases, is
a significant lesson. On an exam I might give a simple electric field
(uniform, or spherically symmetric, or cylindrically symmetric) and expect
them to do some line/surface integral all the way to the end.
Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817