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Figure 22.67To see why an MRI utilizes iron to increase the magnetic field created by a coil, calculate the current needed in a 400 -loop-per-meter circular coil 0.660 $\mathrm{m}$ in radius to create a $1.20-$ field (typical of an MRI instrument) at its center with no iron present. The magnetic field of a proton is approximately like that of a circular current loop $0.650 \times 10^{-15} \mathrm{m}$ in radius carrying $1.05 \times 10^{4} \mathrm{A}$ . What is the field at the center of such a loop?

$1.01 \times 10^{13} \mathrm{T}$

Physics 102 Electricity and Magnetism

Chapter 22

Magnetism

Magnetic Field and Magnetic Forces

Sources of Magnetic field

Electromagnetic Induction

Inductance

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Hope College

University of Winnipeg

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hi. In the given problem, the radius off the loop has been given US 0.650 in tow. 10. Dish par minus 15 m. The current passing through this loop it's supposed to be 1.5 in tow. 10. Dish Park four and peer. Hence, the expression for the magnetic field created at the center of this loop is given us new, not times. I is the current divided by two are. So if we plug in all the known values here form you not. This is four pi into 10 dish par minus seven Tesla Meter or M peered for current. This is 1.5 in tow. 10 days. Part four. NPR finally divided by twice of the radius means two times off 0.650 in tow. 10. This part minus 15 m. So canceling the similar units in numerator and denominator Um, pure with the impure meter with a meter. So finally we get or magnetic field. This is four in 23.14 multiplied by 1.5 and divided by to times off 0.650 into for 10. Dish the power. This is minus seven plus four will give us three, then minus three plus 15. Well, give us 12. So this is the magnetic field. If we calculate it, magnetic field here comes out. Toby 10.1 in tow. 10 dish, part 12, Tesla. Or we can say this is 1.1 in tow. 10 dish, part 13, Tesla. And this is the answer for the given problem. Thank you.

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