Need assistance with Part (a) and Part (b) The magnetic field of a proton is rel

Question

Need assistance with Part (a) and Part (b)

The magnetic field of a proton is relatively close to that of a circular current loop 0.650 times 10^-15 m radius carrying 1.05 times 10^4 A. An MRI machine is required to be able to manipulate these fields. To see why an MRI utilizes iron to increase the magnetic field generated by a coil, calculate the current needed in a 400 loop-per-meter circular coil 0.660 m in radius to generate a 1.20 T field (typical of an MRI instrument) at its center with no iron insert. What is the field at the center of a proton? Notice how it compares to the field we used in the previous calculation.

Explanation / Answer

Part a)

B = u0 * I / ( 2 * r)

Here

u0 = 4 * pi * 10^-7 T*m / A

I = ?

B = 1.2 T

r = 0.65 * 10^-15

then by putting the values

1.2 = (4 * pi * 10^-7) *(400 I ) / (2 * 0.6)

I = 2864.79 A

Part b)

B = u0 * I / ( 2 * r)

Here

u0 = 4 * pi * 10^-7 T*m / A

I = 1.05 * 10^4 amp

r = 0.65 * 10^-15

then by putting the values

B = [ (4 * pi * 10^-7 )* (1.05 * 10^4 ) ] / (2 * 0.65 * 10^-15)

B = 1.0145 * 10^13 T

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