Past exam of the chemistry course of the year 4 of the natural sciences course of the University of Cambridge / 2022 / Paper 3 / Section D / 43 / b / ii / Solution

Expanding the scalar product gives $j_{\alpha }=[n{Q}^2/(2k_{B}T)]{\sum }_{j}f{r}_{ij,\alpha }{\sum }_{\beta }{r}_{ij,\beta }{\mathcal{E}}_{\beta }$. Comparing coefficients of the independently variable field components yieldsThe tensor is symmetric and positive semidefinite because its contraction with any vector twice is a nonnegative sum of squares.