The electric quadrupole is the third term in an electric multipole expansion, and can be defined in MKS by
where
is the permittivity of free space,R is the distance from the collection of charges, and 
is the electric quadrupole moment, which is a tensor.
For a point charge q located at a position R, let the z-axis lie along R, then
But the problem has cylindrical symmetry, so
Furthermore, from the definition of the electric quadrupole moment,
, so
The electric quadrupole potential is therefore
(1)
where
is the permittivity of free space,R is the distance from the collection of charges, and is the electric quadrupole moment, which is a tensor.For a point charge q located at a position R, let the z-axis lie along R, then
(2)
But the problem has cylindrical symmetry, so
Furthermore, from the definition of the electric quadrupole moment,, so(3)
The electric quadrupole potential is therefore
(4)
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