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Some authors claim the Poisson equation is $$\nabla^2 \psi = -\dfrac{\rho}{\epsilon\epsilon_0}$$ (e.g. Wikipedia) whereas other ones (e.g. Andelmann) claim it is $$\nabla^2 \psi = -4\pi\dfrac{\rho}{\epsilon}.$$ I guess $\epsilon_0$ is taken to be one but how would you explain the absence or presence of the $4\pi$ multiplier? Is it related to some choice of units?

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