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### Debye screening in $\mathbb{R^d}$

Consider the Poisson-Boltzmann equation $$\nabla^2 V(r) = -\frac{1}{\epsilon_0}en\left(1 - e^{e V(r)/k_BT}\right)$$ which models the electrostatic potential in a spherically symmetric ideal gas of ...
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### Electric field and electric potential of a point charge in 2D and 1D

in 3D, electric field of a piont charge is inversely proportional to the square of distance while the potential is inversely proportional to distance. We can derive it from Coulomb's law. however, I ...
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### Electric potential due to a point charge in Gaussian/CGS units

I learned electrostatics in SI units. In SI, the electrostatic potential due to a point charge $q$ located at $\textbf{r}$ is given by $\Phi(\textbf{r}) = \frac{q}{4 \pi \epsilon_0 |\textbf{r}|}$. ...
The electric field of a point charge goes like $\displaystyle\frac{1}{r^2}$ The electric field of an infinite line goes like $\displaystyle\frac{1}{s}$ The electric field of an infinite plane is ...