Energy Density of Fields Calculator
Find the energy density stored in electric and magnetic fields.
Electric and magnetic fields store energy per unit volume.
How the Math Works
The Energy Density of Fields Calculator uses the formula u = ½·ε₀·E² + B² ÷ (2·μ₀) to determine the total energy stored in electromagnetic fields per unit volume. Here, ε₀ (permittivity of free space) and μ₀ (permeability of free space) are fundamental physical constants that characterize how electric and magnetic fields interact with the vacuum. The first term, ½·ε₀·E², represents the energy density contributed by the electric field, while the second term, B² ÷ (2·μ₀), accounts for the energy density from the magnetic field. The calculator adds these components to give the total electromagnetic energy density, measured in joules per cubic meter (J/m³).
Practical Applications
This calculation is essential in designing electromagnetic systems across multiple engineering disciplines. Electrical engineers use it to determine energy storage capacity in capacitors and inductors, which are fundamental components in power supplies, radio frequency circuits, and electronic filters. Physicists apply this formula when analyzing electromagnetic wave propagation, such as calculating the energy carried by light, radio waves, or X-rays. It's also crucial for electromagnetic compatibility studies, where engineers must ensure that devices don't emit excessive electromagnetic energy that could interfere with other equipment or violate regulatory standards.
Day-to-Day Use
While you may not calculate field energy densities daily, this principle underlies many technologies you encounter regularly. The wireless charging pads on your phone or laptop rely on magnetic field energy storage and transfer. Wi-Fi routers, cell phone signals, and broadcast television all propagate as electromagnetic waves whose energy density can be calculated using this formula. Even the sunlight carrying energy to Earth's atmosphere and powering solar panels involves the same electromagnetic principles. Understanding energy density helps explain why cell phone signals weaken with distance and why microwave ovens can efficiently heat food by coupling with water molecules.
Worked example
1000 V/m and 0.5 T → about 99,500 J/m³ (almost all magnetic).
FAQ
Where is field energy stored?
In the field itself, throughout the region it occupies.