Respuesta :
Answer:
The magnitude of the magnetic field through the center of this solenoid is 0.0568 T.
Explanation:
Given that,
Length = 15 m
Radius r₁ = 1.6 mm
Resistivity of copper[tex]\rho=1.68\times10^{-8}\ \Omega m[/tex]
Radius [tex]r_{2} =\dfrac{2.5}{2}=1.25\ cm[/tex]
emf = 2.5 V
Length of tube = 0.35 m
We need to calculate the area of cross section
[tex]A = \pi r_{1}^2[/tex]
[tex]A=\pi\times(1.6\times10^{-3})^2[/tex]
[tex]A=0.000008042\ m^2[/tex]
[tex]A=8.038\times10^{-6}\ m^2[/tex]
We need to calculate the resistance
Using formula of resistivity
[tex]R = \dfrac{\rho l}{A}[/tex]
Put the value into the formula
[tex]R=\dfrac{1.68\times10^{-8}\times15}{8.038\times10^{-6}}[/tex]
[tex]R=0.03135\ \Omega[/tex]
We need to calculate the current
Using formula of current
[tex]I=\dfrac{\epsilon}{R}[/tex]
Where, [tex]\epsilon[/tex] = emf
Put the value into the formula
[tex]I=\dfrac{2.5}{0.03135}[/tex]
[tex]I=79.745\ A[/tex]
We need to calculate the number of turns per unit length
Using formula of number of turns
[tex]N=\dfrac{l}{2\pi r_{2}}[/tex]
[tex]N=\dfrac{15}{2\pi\times1.25\times10^{-2}}[/tex]
[tex]N=190.98[/tex]
[tex]n=\dfrac{N}{l}[/tex]
[tex]n=\dfrac{190.98}{0.35}[/tex]
[tex]n=545.65\ turns/m[/tex]
We need to calculate the magnetic field
Using formula of magnetic field
[tex]B=\mu_{0}nI[/tex]
[tex]B=4\pi\times10^{-7}\times545.65\times79.745[/tex]
[tex]B=0.0568\ T[/tex]
Hence, The magnitude of the magnetic field through the center of this solenoid is 0.0568 T.
