⚡ Energy Density of Fields Calculator
Calculate energy density in electric and magnetic fields
Example: 1 × 10⁶ V/m = 1 MV/m
How to Use This Calculator
Select Field Type
Choose whether you want to calculate energy density for an electric field or a magnetic field using the dropdown menu.
Enter Field Value
For electric fields, enter the electric field strength in V/m (or N/C). For magnetic fields, enter the magnetic field strength in Tesla (T). Use scientific notation for very large or very small values.
Calculate
Click the "Calculate Energy Density" button to get the energy density in Joules per cubic meter (J/m³). This represents how much energy is stored per unit volume in the field.
Formula
Electric Field Energy Density
u = (1/2)ε₀E²
Where:
- u = Energy Density (Joules per cubic meter, J/m³)
- ε₀ = Vacuum Permittivity = 8.85 × 10⁻¹² C²/(N⋅m²)
- E = Electric Field Strength (Volts per meter, V/m)
Example: For E = 1 × 10⁶ V/m:
u = 0.5 × 8.85×10⁻¹² × (10⁶)²
u = 4.425 J/m³
Magnetic Field Energy Density
u = B²/(2μ₀)
Where:
- u = Energy Density (Joules per cubic meter, J/m³)
- μ₀ = Vacuum Permeability = 4π × 10⁻⁷ T⋅m/A
- B = Magnetic Field Strength (Tesla, T)
Example: For B = 1 T:
u = (1²) / (2 × 4π × 10⁻⁷)
u = 3.98 × 10⁵ J/m³
Note: Energy density in magnetic fields is typically much higher than in electric fields for comparable field strengths.
About Energy Density of Fields Calculator
The Energy Density of Fields Calculator determines the energy stored per unit volume in electric and magnetic fields. Fields contain energy, and understanding energy density is crucial for analyzing capacitors, inductors, electromagnetic waves, and energy storage systems. The energy density depends on the square of the field strength.
When to Use This Calculator
- Capacitor Design: Calculate energy density in capacitors and understand energy storage capacity
- Inductor Analysis: Determine energy density in magnetic fields around inductors and solenoids
- Electromagnetic Waves: Understand energy transport in electromagnetic radiation
- Energy Storage: Compare energy densities of different field-based energy storage systems
- Physics Education: Learn about field energy and its relationship to field strength
Why Use Our Calculator?
- ✅ Dual Fields: Calculate energy density for both electric and magnetic fields
- ✅ Quick Calculation: Instantly determine energy density from field strength
- ✅ Scientific Notation: Handles very large and very small field values
- ✅ Free Tool: No registration or payment required
- ✅ Educational: Understand how field strength relates to stored energy
Common Applications
Capacitor Energy Storage: Calculate the energy density in capacitors, which is proportional to the square of the electric field. Higher electric fields allow more compact energy storage, making this crucial for designing high-energy-density capacitors used in pulse power systems and energy storage applications.
Superconducting Magnets: Analyze energy density in strong magnetic fields produced by superconducting magnets, used in MRI machines, particle accelerators, and magnetic levitation systems, where understanding energy storage helps with design and safety considerations.
Electromagnetic Wave Energy: Understand how energy is distributed in electromagnetic waves, where electric and magnetic field energy densities are equal and contribute to the total energy flux (Poynting vector) that describes energy transport in radiation.
Tips for Best Results
- Energy density is proportional to the square of field strength - doubling field quadruples energy density
- Magnetic field energy density is typically much higher than electric field energy density for comparable field strengths
- In electromagnetic waves, electric and magnetic energy densities are equal: uE = uB
- For capacitors with dielectric, multiply ε₀ by relative permittivity εr
- Total energy in a volume is U = u × V, where V is volume
Frequently Asked Questions
Why is energy density proportional to the square of field strength?
Energy density depends on field strength squared because energy is work done to establish the field, and work is force times distance. The force on charges depends on field strength, and the field itself is built up gradually, leading to the quadratic relationship u ∝ E² or u ∝ B².
Which has higher energy density, electric or magnetic fields?
For comparable field strengths, magnetic fields typically store much more energy. For example, a 1 T magnetic field has energy density ~4×10⁵ J/m³, while a 1×10⁶ V/m electric field has energy density ~4.4 J/m³. This is why superconducting magnets can store large amounts of energy.
How does energy density relate to capacitor energy?
For a parallel plate capacitor with uniform field E, the energy density is u = (1/2)ε₀E². The total energy is U = u × V = (1/2)ε₀E² × Ad = (1/2)CV², where C is capacitance, V is voltage, A is plate area, and d is separation.
What about energy density in electromagnetic waves?
In electromagnetic waves, the electric and magnetic energy densities are equal: uE = (1/2)ε₀E² = uB = B²/(2μ₀), where E and B are related by E = cB (c is speed of light). The total energy density is u = ε₀E² = B²/μ₀.
How do I calculate total energy from energy density?
Total energy U = ∫ u dV, integrated over the volume. For uniform fields in a volume V, simply multiply: U = u × V. For non-uniform fields, integration is needed to sum energy density contributions throughout the volume.
Does energy density change in materials?
Yes! For electric fields in dielectrics, use ε = εrε₀ instead of ε₀, where εr is relative permittivity. For magnetic fields in materials, use μ instead of μ₀ for magnetic permeability. In diamagnetic and paramagnetic materials, these corrections are small, but in ferromagnetic materials, energy density can be much higher.