Magnetic Energy of solenoid( u=m·B or u=B^2/4pi )

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SUMMARY

The discussion centers on calculating magnetic energy in a solenoid using two formulas: \( u = m \cdot B \) and \( u = \frac{B^2}{4\pi} \). The participant expresses confusion over which formula to apply for their calculations. Additionally, they reference the electromagnetic field-energy density in Gaussian units as \( u = \frac{1}{8 \pi} (\vec{E}^2 + \vec{B}^2) \), indicating a need for clarity on the appropriate context for each formula.

PREREQUISITES
  • Understanding of electromagnetic theory
  • Familiarity with solenoid physics
  • Knowledge of Gaussian units in electromagnetism
  • Basic grasp of energy density calculations
NEXT STEPS
  • Research the application of the formula \( u = m \cdot B \) in solenoid energy calculations
  • Explore the derivation and implications of \( u = \frac{B^2}{4\pi} \)
  • Learn about electromagnetic field-energy density in Gaussian units
  • Investigate the differences between SI and Gaussian unit systems in electromagnetism
USEFUL FOR

Physics students, electrical engineers, and researchers involved in electromagnetism and solenoid applications will benefit from this discussion.

sean1832725142
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Hi,

I have a problem with the fomular
u=m·B
and
u=B^2/4pi
Since I want to calculate how many magnetic energy on a solenoid, I couldn't decide which fomular should I use.
 
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In Gaussian units the electromagnetic field-energy density is given by
$$u=\frac{1}{8 \pi} (\vec{E}^2+\vec{B}^2).$$
 

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