What is the energy density expression for an electromagnetic field in terms of E and B?

What is the energy density expression for an electromagnetic field in terms of E and B?

• A. u = (1/2) ε0 E^2 + B^2 /(2 μ0)
• B. u = ε0 E^2 + B^2/μ0
• C. u = (1/2) μ0 H^2 + (1/2) ε0 E^2
• D. u = (1/2) ε0 E^2 - B^2 /(2 μ0)

Answer: (A)

Energy in an electromagnetic field is stored in two parts: electric and magnetic. The electric part of the energy density is (1/2) ε0 E^2, representing the energy needed to assemble the electric field in a given volume. The magnetic part is (1/2) B^2/μ0, representing the energy stored in the magnetic field. Adding them gives the total energy density: u = (1/2) ε0 E^2 + B^2/(2 μ0). In vacuum, you can also write the magnetic part as (1/2) μ0 H^2 since B = μ0 H, so these forms are equivalent. The standard expression in terms of E and B, however, is the sum of the electric and magnetic contributions with the 1/2 factors, ensuring the energy density remains positive.

Energy in an electromagnetic field is stored in two parts: electric and magnetic. The electric part of the energy density is (1/2) ε0 E^2, representing the energy needed to assemble the electric field in a given volume. The magnetic part is (1/2) B^2/μ0, representing the energy stored in the magnetic field. Adding them gives the total energy density: u = (1/2) ε0 E^2 + B^2/(2 μ0).

In vacuum, you can also write the magnetic part as (1/2) μ0 H^2 since B = μ0 H, so these forms are equivalent. The standard expression in terms of E and B, however, is the sum of the electric and magnetic contributions with the 1/2 factors, ensuring the energy density remains positive.