$($a$)$ A teaching assistant is preparing for an in$-$class demonstration, using insulated copper wire and a power supply. She winds a single layer of the wire on a tube with a diameter of $d_{\text{s}\text{o}\text{l}\text{e}\text{n}\text{o}\text{i}\text{d}}=10\mathrm{.}0cm.$ The resulting solenoid is $l=85\mathrm{.}0cm$ long, and the wire has a diameter of $d_{\text{w}\text{i}\text{r}\text{e}}=0\mathrm{.}100cm.$ Assume the insulation is very thin, and adjacent turns of the wire are in contact. What power $($in W $)$ must be delivered to the solenoid if it is to produce a field of $7\mathrm{.}40$ mT at its center? $($The resistivity of copper is $1\mathrm{.}70{10}^{-8}*m.)$

$$ W

What If$?$ Assume the maximum current the copper wire can safely carry is $22\mathrm{.}0$ A $.$

$($b$)$ What is the maximum magnetic field $($in T $)$ in the solenoid? $($Enter the magnitude.$)$

$$ T

$($c$)$ What is the maximum power $($in W $)$ delivered to the solenoid?

$$ w