MRI (magnetic resonance imaging) is a medical technique that produces detailed \
ID: 1495319 • Letter: M
Question
MRI (magnetic resonance imaging) is a medical technique that produces detailed "pictures" of the interior of the body. The patient is placed into a solenoid that is 40 cm in diameter and 1.2 m long. A 105 A current creates a 5.0 T magnetic field inside the solenoid. To carry such a large current, the solenoid wires are cooled with liquid helium until they become superconducting (no electric resistance).
(a) How much magnetic energy is stored in the solenoid? Assume that the magnetic field is uniform within the solenoid and quickly drops to zero outside the solenoid. _______J
(b) How many turns of wire does the solenoid have? _______
Explanation / Answer
Here ,
radius , r = 40/2 cm
r = 20 cm = 0.20 m
L = 1.2 m
Current , I = 105 A
magnetic field , B = 5 T
a) for the energy stored in magnetic field
Total energy = Volume * energy density of solenoid
Total energy = pi * r^2 * L * 0.5 * B^2/u0
Total energy = pi * 0.20^2 * 1.20 * 0.5 * 5^2/(4pi *10^-7)
Total energy = 1.5 *10^6 J
the total energy stored in the field is 1.5 *10^6 J
b)
let the number of turns is N
as the magnetic field due to solenoid is B
B = u0 * N * I/L
5 = 4pi *10^-7 * N * 105/1.2
solving for N
N = 45472
the number of turns in the solenoid is 45472
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