# Energy stored and # turns in an MRI machine (solenoid)

1. MRI (magnetic resonance imaging) is a medical technique that produces detailed "pictures" of the interior of the body. The patient is placed into a solenoid that is 40 cm in diameter and 1.0 m long. A 100 A current creates a 5.0 T magnetic field inside the solenoid. To carry such a large current, the solenoid wires are cooled with liquid helium until they become superconducting (no electric resistance).

2.U = 0.5LI2
N = l/d

3. L = flux/I = AB/I = 0.00628H
U = 0.5LI2 = 31.4H

N = l/d = 2.5 turns

Am I getting this right?

## Answers and Replies

Is this correct?

Ok, I now know that 31.4H is incorrect. Can someone explain what I'm doing wrong?

Any suggestions?

marcusl
Science Advisor
Gold Member
I see no way to get an exact answer from the information you have provided but you can get close. You can calculate the energy stored in the magnetic field, if you make assumptions about the field (e.g., the field is uniform throughout the solenoid). Your inductance formula then gives the number of turns.