# What is the difference between the potential $V$ and the effective potential $V_{eff}$?

What is the difference between the potential $V$ and the effective potential $V_{eff}$?

Some times when solving problems, an effective potential $V_{eff}$ is defined and its usually equal to the potential $V$ plus other terms. My question why is this potential called an effective potential.

If you take two pinned charges in vacuum for instance, they will interact with a "bare" Coulomb interaction in $\sim 1/r$.
If you put these two charges in a sea of mobile positive and negative charges, they will polarize that medium by interacting with a bare Coulomb potential with all the mobile charges and, if we trace over the degree of freedom of this sea of charges, everything is as if, the two pinned charges interacted with a short ranged screened Coulomb potential in $\sim e^{-\kappa r}/r$.