Question

# The main magnet in an MRI machine is a superconducting solenoid 1.70 m long and 70.0...

The main magnet in an MRI machine is a superconducting solenoid 1.70 m long and 70.0 cm in diameter. During normal operation, the current through the windings is 110 A and the magnetic field magnitude is 1.60 T.

How many turns does the solenoid have?

How much energy is stored in the magnetic field during normal operation?

How much energy is stored if the current is 50.0 A?

a)We know that field inside the solenoid=

where n is numner of turns per meter.

substitutung the values

we get n = 11575 turns per meter

so Number of turns = n X L =19677

b) we know that self inductance of the solenoid is

and then energy stored in the inductor =

putting in the values

so Energy = 1.018 X 106 J

c)

from earlier expression we can observe that energy is directly proportional I2

so

so put I1 = 110 A and E1 = 1.018 X 106 J

I2= 50

so we will get E2 = 0.2 X 106 J

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