Amount of energy stored in a magnetic field

AI Thread Summary
The discussion focuses on calculating the energy stored in the magnetic field of an air-core solenoid with specific dimensions and current. The inductance is calculated using the formula involving the permeability of free space, turns, and length, resulting in a value of approximately 1.3785e-5 H. The energy stored is then computed using the formula U = (1/2) L I^2, yielding about 2.7355 μJ. There is a concern about the correctness of the calculations and the relationships used, particularly regarding the inductance and magnetic field. Clarification is sought on whether the calculations are accurate or if any additional factors need to be considered.
rinarez7
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1. 1. An air-core solenoid with 57 turns is 4.96 cm
long and has a diameter of 1.46 cm.
The permitivity of free space is 4×10−7 T·
m/A.
How much energy is stored in its magnetic
field when it carries a current of 0.634 A ?
Answer in units of μJ.
2.
B = mu-o (I) (N)/ L
Induction= mu-0 (N^2/l) A
U= (1/2) Induction (I ^2)

3. First I calculated Induction= 4pie-7 ( 57turns ^2/ .0496m) (pi(.0146^2))= 1.3785e-5

Then I used U = (1/2) induction (0.634 A ^2)= 2.7355μJ

I am on the wrong path? I thought of calculating the magentic field as well
using my first eqaution= 9.09795 e-4 T but I couldn't find the correct eqaution/ relationship to calculate the energy stored. Thanks in advance for any help!
 
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0.0146 is the diameter, not the radius.
 
My mistake, I did use the diameter/ 2 in my calculations ( just translated it incorrectly) so I still had the same calculation. Is there something else I am missing?
 
Check the calculation of inductance.
 
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