LAPLACE EQUATION IN FRESHMAN PHYSICS

Heat-sensitive liquid crystal sheets are used to observe quantitatively the temperature contours on the surface of an aluminum slab subjected to constant-valued boundary conditions. The experiment is then modeled numerically using spreadsheet techniques. The theoretically derived power series solution to the Laplace equation is given and students use the spreadsheet to numerically investigate its convergence. In a single laboratory session, the introductory physics student studies the Laplace equation from experimental, numerical, and theoretical perspectives.