Can the potential function have a maximum or minimum in free space? Explain.
(N/A) No,the potential function cannot have a maximum or minimum in free space. According to Laplace's equation,$\nabla^2 V = 0$ in a charge-free region. If $V$ had a local maximum or minimum at a point,the Laplacian $\nabla^2 V$ would be non-zero at that point,which contradicts the condition of free space. Physically,this means that a test charge placed in free space will not be in stable equilibrium under the influence of electrostatic forces alone.
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