Electricity & Magnetism
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EM Energy Density

Energy stored per unit volume in EM fields.

Formula

u=12ε0E2+B22μ0u = \tfrac{1}{2}\varepsilon_0 E^2 + \frac{B^2}{2\mu_0}

Variables

EElectric field
BMagnetic field

How it works

This formula tells you how much electromagnetic energy is packed into each cubic metre of space when electric and magnetic fields are present. The two terms come from the field energy stored in the electric field, which grows with E^2, and the magnetic field, which grows with B^2; the constants b50 and bc0 set the scale so the units come out as joules per cubic metre. It is a field-theory result: rather than thinking of energy as belonging to charges or currents alone, Maxwell's theory assigns energy directly to the fields themselves.

When to use it

Use this when you need the energy density of an electromagnetic wave, the field energy in a capacitor or in free space, or when converting between field strength and stored energy. It is especially useful in advanced electromagnetism, optics, and radiation problems.

Worked example, step by step

Find the electromagnetic energy density where the electric field is E = 3.0 10^5 V/m and the magnetic field is B = 1.0 10^-3 T. Step 1: Use u = (1/2)b50E^2 + B^2/(2bc0) Step 2: Compute the electric part: (1/2)(8.85 10^-12)(3.0 10^5)^2 = 0.5 8.85 10^-12 9.0 10^10 = 3.98 10^-1 J/m^3 Step 3: Compute the magnetic part: (1.0 10^-3)^2 / [2(4c0 10^-7)] = 1.0 10^-6 / (2.513 10^-6) = 3.98 10^-1 J/m^3 Step 4: Add them: u = 0.398 + 0.398 = 0.796 J/m^3 Final answer: u  0.80 J/m^3

Common mistakes to avoid

  • Forgetting that the electric term uses E squared, not E itself
  • Using the wrong permeability or permittivity constant, or mixing up b50 and bc0
  • Treating the formula as valid only for waves, when it also applies to static field energy densities

Did You Know?

Empty space carrying an electromagnetic field actually stores energy, which is how sunlight ferries power across the void.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026