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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?

Qmechanic
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Stéphane Laurent
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    It is the choice of units, in particular Gaussian Units. – Kyle Kanos Jul 09 '14 at 13:18
  • Ok thank you @KyleKanos, and this occurs for the unit of $\epsilon$, doesn't it ? – Stéphane Laurent Jul 09 '14 at 13:21
  • More or less. There's a bit more rigorous a proof (involves writing the 4 Maxwell equations in the form $\nabla\cdot\mathbf E=k_1\rho$ etc, together with the Coulomb force to get that replacing $1/\epsilon_0\to4\pi$. – Kyle Kanos Jul 09 '14 at 13:23
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    Possible duplicates: http://physics.stackexchange.com/q/1673/2451 and http://physics.stackexchange.com/q/28673/2451 , http://physics.stackexchange.com/q/74254/2451 and links therein. – Qmechanic Jul 09 '14 at 13:41

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