Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2024 / Paper 2 / 8 / a

The curl of a gradient is zero. Consequently the dot product in the exponent vanishes and

exp [\nabla ϕ \cdot (\nabla \times \nabla ϕ)] = e^{0} = 1 .

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