Answer:
1308 turns per meter
34.57 m
Explanation:
N = Number of turns
L = Length of wire = 0.3 m
r = Radius of wire = 0.014 m
B = Magnetic field = [tex]2.3\times 10^{-2}\ T[/tex]
[tex]\mu_0[/tex] = Vacuum permeability = [tex]4\pi \times 10^{-7}\ H/m[/tex]
Magnetic field at the center of the solenoid is given by
[tex]B=\frac{\mu_0 Ni}{L}\\\Rightarrow \frac{N{L}=\frac{B}{\mu_0 i}\\\Rightarrow \frac{N}{L}=\frac{2.3\times 10^{-2}}{4\pi\times 10^{-7}\times 14}\\\Rightarrow \frac{N}{L}=1307.34417[/tex]
The number of turns will be 1308 per meter
Number of turns would be
[tex]N=1307.34417\times L\\\Rightarrow N=1307.34417\times 0.3\\\Rightarrow N=392.2[/tex]
The total number of turns is 393.
Length of the wire is given by
[tex]l=2\pi r\times N\\\Rightarrow l=2\pi \times 0.014\times 393\\\Rightarrow l=34.57\ m[/tex]
The total length of the wire of the solenoid is 34.57 m
