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    Divergence, Laplacian and curl of $\nabla\frac1r$

    P-TRIV-RA42

    Area
    Real Analysis
    Status
    draft
    Contents

    Consider the vector field \(\vec{A} = \vec{\nabla}\frac{1}{r}\), where \(r = \sqrt{x^2 + y^2 + z^2}\).

    1. Find \(\mathbf{div}\,\vec{A}\), \(\triangle\vec{A}\), \(\mathbf{curl}\,\vec{A}\).

    2. How do the values of \(\mathbf{div}\,\vec{A}\) and \(\triangle\vec{A}\) depend on the choice of coordinate system?

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