Energy Magnetic Field⚠ unverified
Physics / Electromagnetics · Compute the energy stored in a magnetic field over a volume
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| B | B | T | 1.0 | Magnetic flux density |
| V | V | m**3 | 1.0 | Volume occupied by the field |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | U | J | Stored magnetic energy, in joules (J) |
The science & history
Understanding the Parameters
- $B$ — energy scales as $B^{2}$; high-field magnets store large energy (and pose quench hazards).
- $V$ — effective field volume (solenoid bore, gap, etc.).
- $\mu_0$ — $4\pi\times 10^{-7}\,\text{H/m}$ in free space; in linear media use $B^{2}/(2\mu)$.
Derivation (Approaching a Proof)
Inductor energy $U = \tfrac12 L I^{2}$ with $B = \mu_0 n I$ and $L = \mu_0 n^{2} A\ell$ for a long solenoid recovers $U = B^{2} (A\ell)/(2\mu_0)$. Generally the field energy density in free space is $B^{2}/(2\mu_0)$ (or $\tfrac12\mathbf{B}\cdot\mathbf{H}$).
History
Magnetic field energy underpins inductor design, transformers, and MHD / fusion magnet engineering.
Related Concepts: Energy Electric Field, Inductor Energy, Inductance Solenoid, Self Inductance
Notes: Registry calculator energy-magnetic-field (unverified). Free-space uniform-field model.