The Solenoid and the Toroid

A solenoid $60 \mathrm{cm}$ long and of radius $4·0 \mathrm{cm}$ has $3$ layers of windings of $300$ turns each. A $2·0 \mathrm{cm}$  long wire of mass $2·5 \mathrm{g}$ lies inside the solenoid (near its centre) normal to its axis; both the wire and the axis of the solenoid are in the horizontal plane. The wire is connected through two leads parallel to the axis of the solenoid to an external battery which supplies a current of $6·0 \mathrm{A}$ in the wire. What value of current (with an appropriate sense of circulation) in the windings of the solenoid can support the weight of the wire? $\mathrm{g}=9·8{\mathrm{ms}}^{-2}$