A $10-$cm $-$diameter, $1\mathrm{.}0-$m $-$long solenoid is wound with $2000$ turns of superconducting wire. When the magnet is turned on$,$ the current increases from $0$ to Imax in $2\mathrm{.}5$ s $.$ At t $=1\mathrm{.}0$ s $,$ the induced electric field midway between the axis and the windings is $7\mathrm{.}5103$V$/$m $.$What is the solenoid's steady magnetic field strength?