Which expression gives the magnetic energy density u_B?

Which expression gives the magnetic energy density u_B?

• A. u_B = μ0 B^2 / 2
• B. u_B = B^2 /(2 μ0)
• C. u_B = B^2 μ0
• D. u_B = E^2 /(2 μ0)

Answer: (B)

Magnetic energy per unit volume in a vacuum is u_B = B^2/(2 μ0). This comes from the general expression for magnetic energy density, u = (1/2) B H, and the relation in vacuum B = μ0 H. Substituting gives u_B = (1/2) B (B/μ0) = B^2/(2 μ0). The other forms either mix in ε0 or E in a way that isn’t correct for the magnetic part, or place μ0 in the numerator, which isn’t consistent with the correct dependence on B and μ0.

Magnetic energy per unit volume in a vacuum is u_B = B^2/(2 μ0). This comes from the general expression for magnetic energy density, u = (1/2) B H, and the relation in vacuum B = μ0 H. Substituting gives u_B = (1/2) B (B/μ0) = B^2/(2 μ0). The other forms either mix in ε0 or E in a way that isn’t correct for the magnetic part, or place μ0 in the numerator, which isn’t consistent with the correct dependence on B and μ0.