Magnetic resonance imaging needs a magnetic field strength of 1.5 T. The solenoid is 1.8 m long and 75 cm in diameter. It is tightly wound with a single layer of 1.90-mm-diameter superconducting wire.
a. What current is needed?

Respuesta :

Answer:

2270 A

Explanation:

First, the number of turns in the solenoid

[tex]N=\frac {l}{d}[/tex] where l is the length and d is the diameter of a single layer. In this case, the number of turns will be

[tex]N=\frac {1.8}{0.0019}=947.3684211\approx 947[/tex]

The current, I round solenoid will be given by

[tex]I=\frac {BL}{\mu_o N}[/tex] where B is the magnetic field strength, L is the length of solenoid, [tex]\mu_o[/tex] is permeability of free space and N is the number of turns. Taking the permeability of free space as [tex]4\pi\times 10^{-7} H.m^{-1}[/tex]

[tex]I=\frac {1.5\times 1.8}{4\pi\times 10^{-7} H.m^{-1} \times 947}=2270 A[/tex]