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Electricity & Magnetism
Electricity & Magnetism

Energy Density (Magnetic Field)

u=B22μ0u = \frac{B^2}{2\mu_0}

Energy stored per unit volume in a magnetic field.

Variables

u
Energy density
Energy per unit volume
In SI units: kg/(m·s²)
Allowed values: 0 or more
J/m³
B
Magnetic field
Field strength
In SI units: kg/(A·s²)
T
μ₀
Permeability
4π×10⁻⁷
In SI units: kg·m/(A²·s²)
Allowed values: greater than 0
H/m

Derivation

From U = ½LI² and B = μ₀nI, u = B²/(2μ₀).

Your notes

0/5000

Constants in this formula

μ₀
Vacuum Permeability
1.257 × 10⁻⁶. Measured (CODATA 2018).
H/m

Check value

Round inputs run through this page's calculator, with each constant at its tabulated value. Use it to test your own working or a rearranged form. It is a test case, not a real-world example.

  • B = 2 T (Magnetic field)
  • μ₀ = 1.257 × 10⁻⁶ H/m (Permeability)

Result: u = 1.59109 × 10⁶ J/m³

Other electricity & magnetism formulas with the same quantities

Where this formula is listed

Common questions

What is the Energy Density (Magnetic Field) formula?

Energy Density (Magnetic Field) is written u = B²/(2μ₀). Energy stored per unit volume in a magnetic field. It belongs to Electricity & Magnetism, under Magnetism.

What are the units in u = B²/(2μ₀)?

In SI units, u is energy density, measured in kg/(m·s²); B is magnetic field, measured in kg/(A·s²); μ₀ is permeability, measured in kg·m/(A²·s²).

How is the Energy Density (Magnetic Field) formula derived?

From U = ½LI² and B = μ₀nI, u = B²/(2μ₀). The result is u = B²/(2μ₀).