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

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Homework Help Overview

The discussion revolves around the energy stored in the magnetic field of a solenoid used in MRI machines, specifically focusing on the calculations involving inductance and the number of turns in the solenoid. The context includes parameters such as the dimensions of the solenoid, the current flowing through it, and the resulting magnetic field strength.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the formula for energy stored in an inductor and the calculation of inductance based on the solenoid's dimensions and current. There are questions about the correctness of the calculated values and the assumptions made regarding the magnetic field.

Discussion Status

Some participants are questioning the accuracy of the calculations presented, particularly regarding the energy stored and the inductance. Suggestions have been made to consider assumptions about the uniformity of the magnetic field to approach the problem more effectively.

Contextual Notes

There is a recognition that the information provided may not be sufficient to arrive at an exact answer, and assumptions are being discussed as a means to facilitate calculations.

Linus Pauling
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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?
 
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Is this correct?
 
Ok, I now know that 31.4H is incorrect. Can someone explain what I'm doing wrong?
 
Any suggestions?
 
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.
 

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