Consider a clinical MRI ( m agnetic r esonance i maging) superconducting magnet

Question

Consider a clinical MRI (magnetic resonance imaging) superconducting magnet that has a diameter of 0.81 m, length of 1.59 m, and a uniform magnetic field of 2.47 T. Determine

a) the energy density of the magnetic field

b) the total energy in the solenoid.

Consider a clinical MRI (magnetic resonance imaging) superconducting magnet that has a diameter of 0.81 m, length of 1.59 m, and a uniform magnetic field of 2.47 T. Determine a) the energy density of the magnetic field b) the total energy in the solenoid.

Explanation / Answer

The diameter of the magnet d= 0.81m then the radius of the magnet r = 0.405 m the length of the magnet L = 1.59m the uniform magnet field B = 2.47 T (a) The energy density uB = B^2 /2µ0 = (2.47)^2 / 2(4p*10^-7) = 2.4275*10^6 J/m^3 or 2.4275 MJ/m^3 (b) The total energy in the solenoid uB = U/Al therefore the total energy U = uB(Al) = (2.4275*10^6) p(0.405)^2(1.59) = 1.9889*10^6 J or 1.9889 MJ

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