The magnetic field of a proton is very similar to that of a

The magnetic field of a proton is very similar to that of a circular loop (0.650*10^ -15) m in radius carrying (1.05*10^4 A). An MRI machine needs to be able to manipulate these fields.

A.) To see why an MRI utilizes iron to increase the magnetic field produced by a coil, calculate the current required in a 400 loop-per-meter circular coil 0.660 M in radius to produce a 1.20 T field (typical of an MRI instrument) at its center with no iron insert.

B.) What is the field at the center of a proton? Notice how it compares to the field we used in the preivios calculation.

(PLEASE BOLD ANSWER)

Solution

a)

Given N/L =400 turns/m

Magnetic field

B=u_oNI/L

1.2=(4pi*10^-7)*400*I

I=2387.3 A

b)

Magnetic field at the center of the loop

B=u_oI/2R =(4pi*10^-7)*(1.05*10⁴)/2*(0.65*10^-15)

B=1.015*10¹³ T

so

B/B_MRI =(1.015*10¹³)/1.2

B/B_MRI =8.46*10¹²