Magnetic Field Energy Density
u = B² / (2 · µ0)
Quick answer
This calculator solves u = B² / (2 × µ₀) for Energy Density. With Flux Density 0.5 T, the result is 99.47 kJ/m³. It solves in 2 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The energy stored per unit volume in a magnetic field grows with the square of the flux density. This is where an inductor or transformer actually stores its energy—in the field, mostly in the air gap of a gapped core because the low-permeability gap supports a high field. It sets the size of magnetic energy-storage components.
Variables
- u — Magnetic energy density (J/m³)
- B — Magnetic flux density (T)
- µ₀ = 4π×10⁻⁷ H/m —
Practical Notes
In a magnetic material replace µ₀ with µ₀·µr. Because high-µ core material supports little field for a given flux, most inductor energy is stored in the gap—this is why energy-storage inductors are gapped.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| u | Energy Density | J/m³ | mJ/m³, J/m³, kJ/m³ |
| B | Flux Density | T | G, mT, T |
Step by step
- 1. What you know: Flux Density 0.5 T
- 2. The relation: u = B² / (2 × µ₀)
- 3. Substitute: B = 0.5 T
- 4. Result: Energy Density = 99.47 kJ/m³
Worked examples
Minimum range
Given: Flux Density 10 G
Result: Energy Density = 0.3979 J/m³
Low range
Given: Flux Density 10 mT
Result: Energy Density = 39.79 J/m³
Typical
Given: Flux Density 0.5 T
Result: Energy Density = 99.47 kJ/m³
High range
Given: Flux Density 1.5 T
Result: Energy Density = 895.2 kJ/m³
Maximum range
Given: Flux Density 15 T
Result: Energy Density = 89520 kJ/m³
Solving for each variable
Solve for Energy Density
Flux Density 10 G → 0.3979 J/m³
Solve for Flux Density
Energy Density 100 mJ/m³ → 5.013 G
How Energy Density changes with Flux Density
| Flux Density (input) | Energy Density (result) |
|---|---|
| 50 mT | 0.9947 kJ/m³ |
| 125 mT | 6.217 kJ/m³ |
| 0.25 T | 24.87 kJ/m³ |
| 0.375 T | 55.95 kJ/m³ |
| 0.5 T | 99.47 kJ/m³ |
| 0.75 T | 223.8 kJ/m³ |
| 1 T | 397.9 kJ/m³ |
| 2 T | 1592 kJ/m³ |
| 3.5 T | 4874 kJ/m³ |
| 5 T | 9947 kJ/m³ |
The same result in other units
| Unit | Value |
|---|---|
| J/m³ | 99470 |
| kJ/m³ | 99.47 |
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<p><a href="https://vbatpower.com/formulas/magnetic-energy-density/">Magnetic Field Energy Density</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Magnetic Field Energy Density?
Use u = B² / (2 × µ₀). With Flux Density 0.5 T, Energy Density works out to 99.47 kJ/m³.
What is the formula for Magnetic Field Energy Density?
The formula is u = B² / (2 × µ₀). The energy stored per unit volume in a magnetic field grows with the square of the flux density.
How do you find Flux Density when you know the other values?
Rearrange for Flux Density: with Energy Density 100 mJ/m³, Flux Density is 5.013 G.
What units does Magnetic Field Energy Density use?
Energy Density is shown in J/m³, kJ/m³. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
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