We numerically simulated an initially bipolar magnetic field subjected to s
hear motions concentrated near and parallel to the photospheric polarity in
version line. The simulations yield three principal results: (1) For footpo
int displacements comparable to the bipole's depth, the sheared core field
acquires a dipped geometry that can support cool prominence material agains
t gravity. This confirms previous force-free equilibrium models for forming
dipped prominence fields by differential shear and extends them to much la
rger applied shears and time-dependent dynamics with dissipation. (2) At la
rger shears, we discover a new mechanism for forming the helical magnetic f
ields of prominences. It entails a two-step process of magnetic reconnectio
n in the corona. First, flux in the sheared core reconnects with flux in th
e unsheared, restraining arcade, producing new pairs of interlinked field l
ines. Second, as these interlinked fields continue to be sheared, they are
brought together and reconnect again, producing helical field threading and
enveloping the body of the prominence. This mechanism can account for the
twist that is often observed in both quiescent and erupting prominences. (3
) Even for very large shears, the dipped, helical structure settles into an
apparently stable equilibrium, despite the substantial amount of reconnect
ion and twist in the magnetic field. We conclude that neither a kink instab
ility of the helical core held, nor a tether-cutting instability of the res
training arcade, is operating in our low-lying model prominence. This concu
rs with both observations and a theoretical model for prominence stability.