= Planar quadrupole potential
{title2=$V=A(x^2-y^2),\quad\mathbf E=(-2Ax,2Ay,0)$}
This <electric potential> is harmonic and independent of $z$. Its <electric field> is linear in transverse position, with a saddle at the origin. For $A>0$, field lines approach along the $x$ axis and leave along the $y$ axis; off-axis field lines satisfy $xy=\mathrm{constant}$. Equipotentials satisfy $x^2-y^2=\mathrm{constant}$. This is a local planar <electric quadrupole> geometry, not the decaying far field of an isolated three-dimensional quadrupole.
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