What is the energy density of the electric and magnetic fields in vacuum?

What is the energy density of the electric and magnetic fields in vacuum?

• A. u_E = 1/2 ε0 E^2; u_B = B^2 /(2 μ0)
• B. u_E = ε0 E^2; u_B = μ0 B^2
• C. u_E = E^2 /(2 ε0); u_B = B^2 /(2 μ0)
• D. u_E = 1/2 ε0 E^2; u_B = μ0 B^2

Answer: (A)

The energy stored in electromagnetic fields per unit volume splits into electric and magnetic parts, each coming from a term that is quadratic in the field. The general energy density is u = 1/2 E·D + 1/2 H·B. In vacuum, D = ε0 E and H = B/μ0, so the electric part becomes u_E = (1/2) ε0 E^2, and the magnetic part becomes u_B = (1/2) B^2/μ0. This is exactly the form shown: u_E = (1/2) ε0 E^2 and u_B = B^2/(2 μ0). The total energy density is the sum u = (1/2) ε0 E^2 + B^2/(2 μ0). For a plane wave in vacuum, E and B are related by E = cB, which makes the two contributions equal, since 1/(μ0 c^2) = ε0.

The energy stored in electromagnetic fields per unit volume splits into electric and magnetic parts, each coming from a term that is quadratic in the field. The general energy density is u = 1/2 E·D + 1/2 H·B. In vacuum, D = ε0 E and H = B/μ0, so the electric part becomes u_E = (1/2) ε0 E^2, and the magnetic part becomes u_B = (1/2) B^2/μ0. This is exactly the form shown: u_E = (1/2) ε0 E^2 and u_B = B^2/(2 μ0). The total energy density is the sum u = (1/2) ε0 E^2 + B^2/(2 μ0). For a plane wave in vacuum, E and B are related by E = cB, which makes the two contributions equal, since 1/(μ0 c^2) = ε0.