I understand debye length and even the concept of debye shielding, but quantitatively I'm a little confused. If the debye shield has a potential of $$\Phi=\frac{q}{4\pi\epsilon_{0}r}\exp\left({\frac{-r}{\lambda_{D}}}\right)$$ and I insert a positive ion (proton) into a plasma, will the debye length around this ion be the same as the debye length of the plasma? What exactly is $r$ in this equation?
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