The magnitude of the magnetic field in a magnetic resonance imaging (MRI) machin
ID: 1493121 • Letter: T
Question
The magnitude of the magnetic field in a magnetic resonance imaging (MRI) machine can be as great as B = 2.0 T . Under normal circumstances, this field cannot be shut off by just flipping a switch. Instead the magnitude needs to be carefully decreased to zero. In an emergency, however, the magnet can be "quenched" so that B reduces to zero in 20 s. Such a quench can cost thousands of dollars and likely damages the magnets. Assume that the magnetic field exists inside a cylinder of radius R = 300 mm and length = 600 mm .
(A) How much magnetic potential energy is dissipated when the magnetic field is quenched in this way?
(B) What is the average rate at which energy is dissipated?
Explanation / Answer
Here ,
B = 2 T
time ,t = 20 s
r = 300 mm
l = 600 mm
a) for the energy stored in the magnetic field
energy density of magnetic field = 0.5 * B^2/u0
energy density of magnetic field = 0.5 * 2^2/(4pi *10^-7)
energy density of magnetic field = 1.59 *10^6 J/m^3
potential energy stored = energy density * volume
potential energy stored = 1.59 *10^6 * pi * (0.30^2) * 0.600
potential energy stored = 2.7 *10^5 J
the potential energy stored is 2.7 *10^5 J
b)
average rate at which energy is dissipated = potential energy stored/time
average rate at which energy is dissipated = 2.7 *10^5/20
average rate at which energy is dissipated = 1.35 *10^4 W
the average rate at which energy is dissipated is 1.35 *10^4 W
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