Answer
$107.97\ m$
Work Step by Step
Given
Length of the solenoid $L=1.3\ m$
Diameter of the solenoid $d =2.6\ cm = 2.6\times 10^{-2}\ m$
Current carried by the solenoid $i=18\ A$
Magnetic field of a solenoid $B=23\times 10^{-3}\ T$
The field strength at the center of a solenoid having $n$ turns per unit length and carrying current $i$ is given as
$B=\mu_oni$
$n=\frac{B}{\mu_oi}$
$n=\frac{23\times 10^{-3}\ T}{(4\pi\times 10^{-7}H/m)(18\ A)}$
$n=1016.82\ turns/m$
$n$ is the number of turns per unit length
The total number of turns is N, where $N=nL=(1016.82\ turns/m)(1.3\ m) =1321.87\ turns$
Each turn has a circumference of $\pi d =\pi\times 2.6\times 10^{-2}\ m =0.0816\ m $
The total length of wire is then $(1321.87)(0.0816\ m) = 107.97\ m$
