We consider conformal defect solutions in four dimensional $N=2$ gauged
supergravity. These solutions are constructed as a warped product of
$AdS_2\times S^1$ over an interval with non-trivial electric and magnetic
fields. We show for minimal gauged supergravity and for gauged supergravity
with vector multiplets and abelian gauging that supersymmetric defect solutions
are only possible when the geometry has a conical defect in either the bulk or
the boundary metric.