ps02_sol

Ty pically the magnetic induction in a clinic al mri

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Unformatted text preview: nostic ! imaging of tissues in patients. MRI is bas ed on meas uring the res ponse of the weak magnetic dipoles in the atoms of tiss ues under a s trong applied magnetic field. Ty pically, the magnetic induction in a clinic al MRI mac hine may be ~2 Tesla. Consider the materials us ed to fabricat e the MRI chamber that will be placed in the magnetic field, such as aluminum. a. What magnetic field strength is required t o achiev e a 2T induction in the MRI housing if the housing is fabric ated from aluminum? b. Will the magnetization induced in the aluminum be signific ant compared to, say, an iron permanent magnet that has a maximal net magnetization of 1.39x 105 A/ m? Support your ans wer with a calculation. c. What is the work performed by the magnetic field in the volume of a section of the MRI aluminum housing 1 m x 1 m and 5 mm thick ? 3.012 PS 2 5 of 6 10/4/05 a. We use the expression relating field strength H to induction B: B = 2T = µo H + µo M = µo (1 + " ) H From the class notes, we hav e the susceptibility for Al: " = 2.07 # 10$5 ! = 2T = 2 kg = ' 4 & # 10$7 kg % m * 1 + 2.07 # 10$5 H B ) ,( ) s% C ( C2 + C A - H = 1.59 # 10 6 = 1.59 # 10 6 m% s m b. The magnetization is calc ulated directly: ! M = "H = 32.9 A m …this is only 0.02% of the magnetization of the example iron permanent magnet! c. The work is: ! 1.59"10 6 w= # VµHdH = Vµ (1 + $ ) o 0 H2 2 1.59"10 6 0 = 7, 942 J ! 3.012 PS 2 6 of 6 10/4/05 0 0.05 0.04 0.03 0.02 0.01 0 0 5 10 15 20...
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