Discussion
The Laplacian of the potential in a charge-free region is
Answer: B
Taking the divergence of the gradient relation and using the vanishing divergence of D in a charge-free region gives \( \nabla^2 V = 0 \). Where charge is present the right hand side becomes minus the density over the permittivity, and the equation is then Poisson's, which is the subject of the next topic in this series.
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