Given data:
* The magnetic field inside the solenoid is,
[tex]\begin{gathered} B=17.5\text{ mT} \\ B=17.5\times10^{-3}\text{ T} \end{gathered}[/tex]* The length of the solenoid is,
[tex]\begin{gathered} l=12\text{ cm} \\ l=12\times10^{-2}\text{ m} \end{gathered}[/tex]* The current through the solenoid is,
[tex]\begin{gathered} I=250\text{ mA} \\ I=250\times10^{-3}\text{ A} \end{gathered}[/tex]Solution:
The magnetic field inside the solenoid is,
[tex]B=\mu_oNI[/tex]where N is the number of turns in the solenoid,
[tex]\mu_o\text{ is the permeability of free space}[/tex]Substituting the known values,
[tex]\begin{gathered} 17.5\times10^{-3}=4\pi\times10^{-7}\times N\times250\times10^{-3} \\ 17.5\times10^{-3}=3141.59\times10^{-10}\times N \\ N=\frac{17.5\times10^{-3}}{3141.59\times10^{-10}} \\ N=0.00557042\times10^{-3+10} \\ N=0.00557042\times10^7 \\ N=55.7042\times10^3 \\ N=55704.2 \\ N\approx55704 \end{gathered}[/tex]Thus, the number of turns in the solenoid is 55704.
