Electromagnetic Field Energy Density Calculator
Permittivity Of Vacuum
Electric Field
Magnetic Flux Density
Permeability of Vacuum
Electromagnetic Field: {{electromagneticFieldResult()}}

Formula:

u = ((1/2)ε0E2) + ((1/2)*(B2/μ0))

Where,

u = Electromagnetic Field

εo = Permittivity Of Vacuum

E = Electric Field

B = Magnetic Flux Density

μo = Permeability Of Vacuum

Frequently Asked Questions

What is electromagnetic field energy density and why does it matter?

Electromagnetic field energy density (u) quantifies how much energy is stored per unit volume in electromagnetic fields. Electric fields store energy through polarization (u_E = ½ε₀E²), while magnetic fields store energy through magnetization (u_B = ½B²/μ₀). Total energy density is their sum. This concept is fundamental for understanding energy transport in electromagnetic waves, capacitor/inductor energy storage, and power flow in transmission lines.

How do electric and magnetic energy densities compare in electromagnetic waves?

In electromagnetic waves propagating through free space, electric and magnetic energy densities are equal: u_E = u_B. Since the total energy density equals 2u_E, both fields contribute equally to wave energy. The wave carries power according to the Poynting vector S = (1/μ₀)E × B. This equal energy partitioning is a characteristic feature of electromagnetic waves and shows the deep connection between E and B fields.

When are electric versus magnetic energy density dominant?

In static electric fields near capacitors and conductors, electric energy dominates. In magnetic field regions near inductors and permanent magnets, magnetic energy dominates. In propagating electromagnetic waves, they’re equal. In materials, relative dominance depends on applied fields. Understanding which energy dominates is crucial for design of energy-efficient systems and understanding loss mechanisms in electromagnetic devices.

What are practical implications of electromagnetic energy density calculations?

Energy density determinesHow much energy can be stored per unit volume (important for capacitor/inductor design), guides field strength limits before breakdown (especially in dielectrics near capacitor plates), helps calculate radiation pressure (E + B fields exert pressure on surfaces), and predicts power dissipation in conductors. These calculations are essential for high-voltage system design and plasma confinement.

How does energy density relate to wave propagation and Poynting vector?

The Poynting vector S = (1/μ₀)E × B describes electromagnetic power flow (energy per unit time per unit area). This relates to energy density through wave velocity: energy flows at speed c for electromagnetic waves. High energy density regions represent concentrated electromagnetic field energy. Understanding this relationship is essential for antenna design, laser physics, and microwave engineering.

Physical Basis & References

This calculator applies Energy Density in Electromagnetic Fields:

$$u = \frac{1}{2}\varepsilon_0 E^2 + \frac{1}{2\mu_0}B^2$$

For electromagnetic waves: $u_{total} = \frac{1}{c}S$ where S is the Poynting vector magnitude

Key Physics Principles:

  • Energy Conservation - Field energy represents stored electromagnetic energy
  • Poynting Vector - Energy flow vector S = (1/μ₀)E × B
  • Maxwell Equations - Describe how fields create and store energy
  • Wave Energy - Propagating electromagnetic waves carry energy at speed c

Key Assumptions:

  • Linear, isotropic media with ε₀ and μ₀
  • Static or quasi-static fields
  • No absorption or dissipation (ideal media)
  • Uniform field distribution (local calculation)
  • Classical electromagnetism (non-quantum)

Typical Range of Values:

  • Electric field: 0 to 10⁷ V/m (before air breakdown)
  • Magnetic flux density: 0 to 10 T (achievable with conventional magnets)
  • Energy density: 0 to 10⁸ J/m³ (depending on field strengths)
  • Poynting vector magnitude: 0 to 10¹¹ W/m² (intense laser focus)

Further Reading:

  • Jackson, J.D. (1998). Classical Electromagnetism, 3rd Edition. Wiley.
  • Griffiths, D.J. (2013). Introduction to Electrodynamics, 4th Edition. Pearson.
  • Electromagnetic Energy and Poynting Vector - MIT OpenCourseWare