Question

The main magnet in an MRI machine is a superconducting solenoid 2.0 m long and 33 cm in radius. During normal operation, the current through the windings is 81 A, and the resistance of the windings is zero. The inductance of the solenoid is 89 H.
(a) Calculate the turns per meter of the solenoid.
(b) Calculate the magnitude of the magnetic field generated by the MRI machine during normal operations.
(c) Calculate the magnetic flux through a single turn of the solenoid.
(d) Calculate the energy density of the magnetic field within the solenoid.
(e) The magnet is started by connecting the solenoid to a 20 V power supply. Determine how long it takes for the current to go from zero to 81 A.

Answer 1

per unit ans: l=2m r=0.33m I=8iA L=894 [where in a) now inductance is given by L= Monzaral is number 1 * 89=42x107x n² x ax (0-33)² x 2 of turns > in:1.01x104 /m] length] b) B = Mon I : 48x 10-7 X 1.01x104 x 81 [B=1.028T c) D = Bar?- 1.028x*(0.33)2 -10:35 wbl d) E = y kho B? =\_LI? = 1,X99x812 - 291964.5 5/ma [E = 291.9 X1033 /m3]