A $12-$cmcm$-$diameter, $1\mathrm{.}0-$mm$-$long solenoid is wound with $2000$ turns of superconducting wire. When the magnet is turned on$,$ the current increases from $0$ to ImaxImax in $2\mathrm{.}5$ ss$.$ At tt $=1\mathrm{.}0$ ss$,$ the induced electric field midway between the axis and the windings is $7\mathrm{.}5103$V$/$m$7\mathrm{.}5103$V$/$m$.$What is the solenoid's steady magnetic field strength?