Energy Stored in Magnetic Field of Solenoid

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SUMMARY

The discussion focuses on calculating the energy stored in the magnetic field of a solenoid with a length of 39.9 cm and a diameter of 2.00 cm, resulting in a magnetic field strength of 0.800 T. The formula used for energy storage is U = (1/2)(B^2)(area*length)/(μ), where μ represents the permeability of free space. The user initially calculated the energy as 45.324 J but realized an error in the permeability value used in the calculation. Correcting this value is crucial for obtaining an accurate result.

PREREQUISITES
  • Understanding of solenoid physics and magnetic fields
  • Familiarity with the formula for energy stored in a magnetic field
  • Knowledge of permeability of free space (μ = 8.85 x 10^-7 T·m/A)
  • Basic proficiency in algebra and unit conversions
NEXT STEPS
  • Review the derivation of the energy storage formula U = (1/2)(B^2)(area*length)/(μ)
  • Learn about the properties of magnetic fields in solenoids
  • Explore the implications of permeability in electromagnetic calculations
  • Practice solving energy storage problems in different geometries of magnetic fields
USEFUL FOR

Students studying electromagnetism, physics educators, and anyone interested in understanding energy storage in magnetic fields, particularly in solenoids.

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Homework Statement


The magnetic field inside an air-filled solenoid 39.9cm long and 2.00cm in diameter is 0.800T. Approximately how much energy is stored in this field?


Homework Equations



U=(1/2)LI^2
=> U = (1/2)(B^2)(area*length)/(u)

The Attempt at a Solution


I discovered how to derive the bottom equation from the top equation from http://hyperphysics.phy-astr.gsu.edu/HBASE/electric/indeng.html#c2

The derivation on the site seems to make sense, but when I try to use the bottom equation I get:
U = (1/2)(0.8^2)(Pi*0.01^2)*(0.399)/(8.85*10^-7) = 45.324 J

What am I missing here?

Thanks,
x^2
 
Physics news on Phys.org
Check the value you use for permeability.
 
Kurdt said:
Check the value you use for permeability.

Oh wow do I feel stupid now... Thanks for the help!
x^2
 

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