Energy Density of a magnetic field

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SUMMARY

The energy density of a magnetic field can be calculated using the formula u = B^2 / (2μ0), where B is the magnetic field strength in Tesla and μ0 is the permeability of free space, defined as 4π × 10^-7 N/A². For a magnetic field of 0.03 T, the correct calculation yields an energy density of 0.000225 J/m³, not 358.1 A/m. It is essential to maintain consistency in SI units throughout the calculation to achieve accurate results.

PREREQUISITES
  • Understanding of magnetic field strength (Tesla)
  • Familiarity with the permeability of free space (μ0)
  • Knowledge of energy density concepts (Joules/m³)
  • Basic proficiency in unit conversions within the SI system
NEXT STEPS
  • Review the derivation of the energy density formula for magnetic fields
  • Study the properties and applications of the magnetic constant (μ0)
  • Explore unit conversion techniques in the SI system
  • Investigate the relationship between magnetic fields and energy density in electromagnetic theory
USEFUL FOR

Physicists, electrical engineers, and students studying electromagnetism who need to understand the calculations related to magnetic fields and energy density.

Macarenses
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I'm trying to calculate the energy density of a given magnetic field (0.03 T). I'm supposed to use the equation u=B^2/2μ right? Well I'm getting 358.1 A/m (?). Something is wrong here.

Thanks in advance.
 
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Magnetic units can be confusing. You might try reading the Wikipedia articles below.

Or you can take it on faith that if you use SI units throughout, the answer will come out in SI units. In this case, B is in Tesla (which can also be written as Newtons/(Amp-Meter)), and μ0 = 4π*10^-7 Newtons/Amp^2, then the answer U = B^2/(2μ0) will come out in Newtons/m^2, which is the same as Joules/m^3 - i.e an energy density.

http://en.wikipedia.org/wiki/Magnetic_constant
http://en.wikipedia.org/wiki/Tesla_(unit)
 

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