  Recently solar flares exhibiting a double J-shaped ribbons in the lower solar
atmosphere have been paid increasing attention in the context of extending the
two-dimensional standard flare model to three dimensions, as motivated by the
spatial correlation between photospheric current channels and flare ribbons.
Here we study the electric currents through the photospheric area swept by
flare ribbons (termed synthesized ribbon area or SRA), with a sample of 71
two-ribbon flares, of which 36 are J-shaped. Electric currents flowing through
one ribbon are highly correlated with those through the other, therefore
belonging to the same current system. The non-neutrality factor of this current
system is independent of the flare magnitude, implying that both direct and
return currents participate in flares. J-shaped flares are distinct from
non-J-shaped flares in the following aspects: 1) Electric current densities
within J-shaped SRA are significantly smaller than those within non-J-shaped
SRA, but J-shaped SRA and its associated magnetic flux are also significantly
larger. 2) Electric currents through SRA are positively correlated with the
flare magnitude, but J-shaped flares show stronger correlation than
non-J-shaped flares. 3) The majority (75\%) of J-shaped flares are eruptive,
while the majority (86\%) of non-J-shaped flares are confined; accordingly,
hosting active regions of J-shaped flares are more likely to be sigmoidal than
non-J-shaped flares. Thus, J-shaped flares constitute a distinct subset of
two-ribbon flares, probably the representative of eruptive ones. Further, we
found that combining SRA and its associated magnetic flux has the potential to
differentiate eruptive from confined flares.
