Energy Density of Fields Calculator

Calculate energy density stored in electric and magnetic fields using electromagnetic field theory

Calculate Energy Density

Electric field strength in the medium

Magnetic flux density in the medium

Select the material/medium

Select desired unit for energy density output

Energy Density Results

0.000e+0
J/m³
Electric Field Energy
0.000e+0
J/m³
Magnetic Field Energy
0.000e+0
J/m³
Total Energy Density
Medium: Vacuum/Air
Electric Formula: uₑ = (ε/2)E²
Magnetic Formula: uₘ = B²/(2μ)
Total in J/m³: 0.000e+0
Permittivity: 8.854e-12 F/m
Permeability: 1.257e-6 H/m

Energy Density Analysis

Example Calculation

Electromagnetic Wave

Electric Field: 2,000 N/C

Magnetic Field: 6.67 × 10⁻⁶ T

Medium: Vacuum

Calculation

uₑ = (ε₀/2)E² = (8.854×10⁻¹²/2)×(2×10³)²

uₘ = B²/(2μ₀) = (6.67×10⁻⁶)²/(2×4π×10⁻⁷)

Total: 1.77 × 10⁻⁵ J/m³

Key Formulas

1

uₑ = (ε/2)E²

Electric field energy density

ε = permittivity of medium

2

uₘ = B²/(2μ)

Magnetic field energy density

μ = permeability of medium

3

u = uₑ + uₘ

Total energy density

Sum of electric and magnetic components

Physical Constants

Vacuum permittivity (ε₀)8.854 × 10⁻¹² F/m
Vacuum permeability (μ₀)4π × 10⁻⁷ H/m
Speed of light (c)2.998 × 10⁸ m/s
Water εᵣ≈ 81
Glass εᵣ≈ 7

Understanding Energy Density of Fields

What is Energy Density?

Energy density is the amount of energy stored per unit volume in a medium. Electric and magnetic fields can store energy, which is fundamental to understanding electromagnetic waves, capacitors, inductors, and many other electromagnetic phenomena.

Types of Field Energy

  • Electric Field Energy: Stored in capacitors, around charged objects
  • Magnetic Field Energy: Stored in inductors, around magnets and currents
  • Electromagnetic Waves: Light, radio waves contain both types

Mathematical Foundation

u = (ε/2)E² + B²/(2μ)

Total energy density formula

u:Energy density (J/m³)
ε:Permittivity of medium (F/m)
E:Electric field strength (N/C or V/m)
B:Magnetic flux density (T)
μ:Permeability of medium (H/m)

Note: Energy density behaves like pressure - it exerts force on boundaries and can drive electromagnetic phenomena.

Electromagnetic Waves

In electromagnetic waves (like light), energy oscillates between electric and magnetic forms. The total energy density determines the intensity of the wave.

Capacitors & Inductors

Capacitors store energy in electric fields between plates. Inductors store energy in magnetic fields around coils. Both are essential components in electronics.

Practical Applications

Understanding field energy density is crucial for designing antennas, MRI machines, particle accelerators, and energy storage systems.