$($a$)$

A physicist is constructing a solenoid. She has a roll of insulated copper wire and a power supply. She winds a single layer of the wire on a tube with a diameter of

dsolenoid $=10\mathrm{.}0$ cm$.$

The resulting solenoid is

$=70\mathrm{.}0$ cm

long, and the wire has a diameter of

dwire $=0\mathrm{.}100$ cm$.$

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 $8\mathrm{.}20$ mT at its center? $($The resistivity of copper is $1\mathrm{.}70108$ 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