A single$-$turn square loop of side LL is centered on the axis of a long solenoid. In addition, the plane of the square loop is perpendicular to the axis of the solenoid. The solenoid has $1350$ turns per meter and a diameter of $5\mathrm{.}55$ cmcm $,$ and carries a current of $2\mathrm{.}75$ AA $.$ Find the magnetic flux through the loop when L$=$L$=2\mathrm{.}90$ cmcm $.$ Find the magnetic flux through the loop when L$=$L$=5\mathrm{.}55$ cmcm $.$ Find the magnetic flux through the loop when L$=$L$=12\mathrm{.}0$ cmcm $.$