(A) The magnitude of the magnetic field in a magnetic resonance imaging (MRI) ma

Question

(A)

The magnitude of the magnetic field in a magnetic resonance imaging (MRI) machine can be as great as B = 3.0 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 l = 400 mm . What is the average rate at which energy is dissipated? Express your answer with the appropriate units.

Explanation / Answer

apply the fomula for magnetic energy density u = eenrgy/Volume = B^2/2uo

where B is magnetic field

uo is 4pi e-7

V is Volume = pi r^2 l

so

Eenergy = B^2* V/2uo

magnetic energy U = 3*3 * 3.14 * 0.3*0.3 * 0.4 /(2* 3.14 e-7)

U = 1.62 *10^6 Joules

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