Which expression correctly defines magnetic reluctance Rm?

Which expression correctly defines magnetic reluctance Rm?

• A. Rm = μ A / l
• B. Rm = l μ / A
• C. Rm = l/(μ A)
• D. Rm = A l μ

Answer: (C)

Magnetic reluctance is the opposition that a magnetic path offers to the flow of magnetic flux, analogous to resistance for electric current. For a uniform path of length l and cross-sectional area A in a material with permeability μ, the relationship between the magnetomotive force F (in ampere-turns) and the flux Φ (in webers) follows F = Rm Φ, where Rm is the reluctance. If the path is uniform, H is the same along its length, so F = H l. The flux is Φ = B A, and B = μ H, so Φ = μ H A. Substituting H = F / l into Φ gives Φ = μ A (F / l), which rearranges to F = (l / (μ A)) Φ. Thus the reluctance is Rm = F / Φ = l / (μ A). This shows the correct form: reluctance grows with longer path length and decreases with larger cross-sectional area or greater permeability. The other expressions would either place μ and A in the numerator or mix up the factors, which would not match the derived relation or yield the wrong units.

Magnetic reluctance is the opposition that a magnetic path offers to the flow of magnetic flux, analogous to resistance for electric current. For a uniform path of length l and cross-sectional area A in a material with permeability μ, the relationship between the magnetomotive force F (in ampere-turns) and the flux Φ (in webers) follows F = Rm Φ, where Rm is the reluctance.

If the path is uniform, H is the same along its length, so F = H l. The flux is Φ = B A, and B = μ H, so Φ = μ H A. Substituting H = F / l into Φ gives Φ = μ A (F / l), which rearranges to F = (l / (μ A)) Φ. Thus the reluctance is Rm = F / Φ = l / (μ A).

This shows the correct form: reluctance grows with longer path length and decreases with larger cross-sectional area or greater permeability. The other expressions would either place μ and A in the numerator or mix up the factors, which would not match the derived relation or yield the wrong units.