What is the magnetic energy density in a linear material in terms of B and μ?

• A. u = B^2 /(2 μ)
• B. u = μ B^2 / 2
• C. u = B /(2 μ)
• D. u = μ /(2 B)

Answer: (A)

Magnetic energy density is the energy per unit volume stored in the magnetic field, given by u = (1/2) B H. In a linear material, B = μ H, so H = B/μ. Substituting into the expression gives u = (1/2) B (B/μ) = B^2 /(2 μ). This shows that for a fixed magnetic flux density B, increasing the material’s permeability μ reduces the stored energy density, since the field is more easily established. The alternative form μ B^2 / 2 would imply energy increasing with μ, which isn’t correct for a fixed B.