 Solution

ID: past-exam-of-the-mathematical-methods-ii-course-of-the-university-of-oxford/2018/9/b/solution

C \times (J \times r) = J (C \cdot r) - r (C \cdot J) .

For the

i

C^{'} = e_{i}

gives

\int_{V} r_{i} (C \cdot J) d V = - \int_{V} (C \cdot r) J_{i} d V

. Thus the two terms on the right have opposite integrals. Consequently

\int_{V} (C \cdot r) J d V = \frac{1}{2} C \times \int_{V} (J \times r) d V .

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