For a class demonstration, a professor needs to create a solenoid using copper wire with diameter d $=0\mathrm{.}500$ mm$.$ The resistance of the solenoid needs to be $3\mathrm{.}50$ and the magnetic field of the solenoid with a current of $2\mathrm{.}10$ A should be $4\mathrm{.}70102$ T$.$ Assume the resistance does not change significantly with temperature, and the radius of the solenoid is $1\mathrm{.}00$ cm$.($Use

$=1\mathrm{.}70108$ m

for the resistivity of copper.$)$

$($a$)$

How many turns of wire does the professor need?

turns

$($b$)$

Determine the required length $($in cm$)$ of the solenoid.

cm