Past exam of the mathematics course of the year 2 of the natural sciences course of the University of Cambridge / 2015 / Paper 2 / 3 / a

Solution

F = ϕ \nabla ψ - ψ \nabla ϕ

\nabla \cdot F = \nabla ϕ \cdot \nabla ψ + ϕ \nabla^{2} ψ - \nabla ψ \cdot \nabla ϕ - ψ \nabla^{2} ϕ = ϕ \nabla^{2} ψ - ψ \nabla^{2} ϕ .

\int_{V} (ϕ \nabla^{2} ψ - ψ \nabla^{2} ϕ) d V = \int_{S} (ϕ n \cdot \nabla ψ - ψ n \cdot \nabla ϕ) d S .

The fields and boundary are assumed sufficiently regular; a Green-function singularity is handled by excising a small ball or by using distributions.

There are no discussions about this article yet.

There are currently no matching articles.