Energy Density of Electric and Magnetic Fields
Calculate energy density of electric and magnetic fields using u = ½ε₀E² + ½B²/μ₀. Free online physics calculator with accurate J/m³ results, interactive charts, and breakdown tables.
About This Calculator
The Energy Density of Electric and Magnetic Fields Calculator computes the amount of energy stored per unit volume in electromagnetic fields using the fundamental physics formula u = ½ε₀E² + ½B²/μ₀. This calculator is designed for physics students, electrical engineers, researchers, and anyone studying electromagnetism who needs to quickly compute field energy densities.
Electric fields store energy proportional to the square of the field strength scaled by the vacuum permittivity ε₀ (8.854 × 10⁻¹² F/m). Magnetic fields store energy proportional to the square of the field strength scaled by the inverse of the vacuum permeability μ₀ (4π × 10⁻⁷ H/m). The total energy density is the sum of both contributions, expressed in joules per cubic meter (J/m³). For an electromagnetic wave in vacuum, the electric and magnetic energy densities are equal, and the total energy density relates to the wave intensity through the Poynting vector.
Applications
Capacitors: The energy stored in a parallel-plate capacitor is U = uE × volume = ½ε₀E² × Ad, where A is plate area and d is plate separation. High-energy-density capacitors are crucial for pulsed power systems, electric vehicles, and power electronics.
Inductors and magnets: Magnetic energy density determines the energy storage capacity of inductors, electromagnets, and superconducting magnetic energy storage (SMES) systems. The formula uB = ½B²/μ₀ shows that doubling the magnetic field quadruples the energy density.
Electromagnetic waves: Sunlight and all electromagnetic radiation carry energy through oscillating electric and magnetic fields. The intensity I of an EM wave relates to energy density by I = c·u, where c is the speed of light. This principle underlies everything from radio communications to laser cutting.
How to use
Enter the electric field strength in volts per meter (V/m) and the magnetic field strength in teslas (T). Leave a field at zero if you only want to compute one component. The calculator will display the electric energy density, magnetic energy density, total energy density, and a visual breakdown using charts.
Frequently Asked Questions
What is energy density of electric and magnetic fields?
Energy density is the amount of energy stored per unit volume in an electric or magnetic field. For electric fields, uE = ½ε₀E². For magnetic fields, uB = ½B²/μ₀. The total energy density is the sum of both contributions, measured in joules per cubic meter (J/m³).
What are the units of electric field and magnetic field inputs?
Electric field strength is entered in volts per meter (V/m), which is equivalent to newtons per coulomb (N/C). Magnetic field strength is entered in teslas (T). The result is given in joules per cubic meter (J/m³).
What are the constants ε₀ and μ₀ used in the formula?
ε₀ is the vacuum permittivity, approximately 8.854 × 10⁻¹² F/m. μ₀ is the vacuum permeability, exactly 4π × 10⁻⁷ H/m. These are fundamental physical constants that determine how electric and magnetic fields propagate through empty space.
How does energy density relate to electromagnetic waves?
In an electromagnetic wave, energy is equally shared between the electric and magnetic fields. The total energy density determines the intensity of the wave. For light and other EM radiation, the Poynting vector S = c·u gives the power per unit area carried by the wave.
Can this calculator handle zero electric or magnetic field?
Yes. If you enter zero for one field, the calculator computes the energy density contribution from only the non-zero field. For example, entering E = 0 and B = 1 T gives only the magnetic field energy density of approximately 397,887 J/m³.
What is the energy density of Earth's magnetic field?
Earth's surface magnetic field is about 25 to 65 μT. Using B = 50 μT = 5 × 10⁻⁵ T, the magnetic energy density is approximately 0.001 J/m³. This is very small compared to typical laboratory fields.
How is energy density used in capacitor design?
In a parallel-plate capacitor, the energy stored in the electric field is U = ½CV² = ½ε₀E² × volume. The energy density uE = ½ε₀E² tells engineers how much energy can be stored per unit volume, which is critical for designing compact, high-energy-density capacitors for power electronics.