SHOW ALL WORK 1) A MRI is a medical device that measures the atomic spin of wate
ID: 1495611 • Letter: S
Question
SHOW ALL WORK 1) A MRI is a medical device that measures the atomic spin of water molecules in the body. To achieve this it must submit the body to an extremely powerful magnetic field. This field is created by a solenoid that is 199 cm long, with a cavity 60 cm wide. It is wrapped with a single layer of AWG 14 gauge wire loops. A) Within the machine the MRI creates a magnetic field of 1.7 Tesla. How much current is flowing through the MRI machine. B) The magnetic field produced by an MRI machine is large enough to be dangerous because they induce a current into ferromagnetic materials and can cause them to heat up or become magnetized. A paperclip sitting on a table 3.4 m from the mouth of the solenoid. The loop of the paperclip has an induced current of 1.5 amps. And accelerates to 22 mph in 0.4 seconds. Determine the magnetic field at the paperclip from the MRI machine.
Explanation / Answer
d = 1.628 mm [ FOR awg 14 GAUGE]
a) B = 1.7 T
B for a solenoid = mu*NI/L
L = 1.99 m
D = 0.6m
N = 1.99/d = 1.99/1.628*10^-3 m
1.7 = mu*1.99*I/1.628*10^-3 *1.99 = 4*3.14*10^-7*I/1.628*10^-3
I = 2203.503 A
b) I = 1.5 A
v = 22 mph = 9.83488 m/s = u + at = 0 + a*0.4
a = 24.5872 m/s/s
F = ma = BIL
B = ma/IL = m*24.5872/1.5L = 16.3914 (lambda) T
where lambda is mass per unit length of the clip
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