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16. To generate a uniform 2T magnetic field for an MRI machine with a coil of...

16. To generate a uniform 2T magnetic field for an MRI machine with a coil of diameter 50 cm and 10 000 turns over the 1 m distance of the coil,

(a) Solve for the current through the coil needed to create this large magnetic field. /2

(b) Approximate the total length of wire needed to produce 10 000 turns of this radius. /2

(c) If we need to keep the resistive power emitted by this coil under 1000 W so that the patient is not uncomfortable, what is the maximum resistance allowable by the coil? /2

(d) If the cross-sectional area of the wire used is 7.85 ×10−9 m2 , find the maximum resistivity of wire that could be used to meet your criterion found in part (c). /2 15

(e) Copper has one of the lowest room temperature resitivities of all metals at ρ = 1.7 × 10−8Ω m. Could an MRI machine with these requirements be made to operate with copper wire at room temperature as its coil? How is this avoided in real MRI machines?

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