Answer:
The number of turns is [tex]N = 1750 \ turns [/tex]
Explanation:
From the question we are told that
The inner radius is [tex]r_i = 12.0 \ cm = 0.12 \ m[/tex]
The outer radius is [tex]r_o = 15.0 \ cm = 0.15 \ m[/tex]
The current it carries is [tex]I = 1.50 \ A[/tex]
The magnetic field is [tex]B = 3.75 mT = 3.75 *10^{-3} \ T[/tex]
The distance from the center is [tex]d = 14.0 \ cm = 0.14 \ m[/tex]
Generally the number of turns is mathematically represented as
[tex]N = \frac{2 * \pi * d * B}{ \mu_o * r_o }[/tex]
Generally [tex]\mu_o[/tex] is the permeability of free space with value
[tex]\mu_o = 4\pi * 10^{-7} \ N/A^2[/tex]
So
[tex]N = \frac{2 * 3.142 * 0.14 * 3.75 *10^{-3} }{ 4\pi * 10^{-7} * 0.15 }[/tex]
[tex]N = 1750 \ turns [/tex]
