\[u_B=\frac{B^2}{2\mu_0}\]
Variables
uBmagnetic energy density (J/m³)
Bmagnetic field strength (T)
mu0vacuum permeability (H/m)
Description
What is this formula?
This formula calculates the magnetic energy stored per unit volume inside a magnetic field. The energy density depends on the magnetic field intensity and the magnetic permeability of the medium.
When to use it
Use this equation when studying electromagnetic energy storage, inductors, magnetic confinement systems, and magnetic field energetics.
Example
Calculate the magnetic energy density for a magnetic field of 0.6 T.
Data:
B = 0.6 T
mu0 = 4*pi*10^-7 H/m
Formula:
uB = B²/(2*mu0)
Substitution:
uB = (0.6²)/(2*(4*pi*10^-7))
Result:
uB = 1.43 × 10^5 J/m³
Applications
- Magnetic energy storage
- Electromagnetic field analysis
- Inductor design
- Plasma confinement
- Electromechanical systems