Calculate magnetic reluctance from geometry and permeability A core has length l = 0.045 m, cross-sectional area A = 0.015 m², and material permeability μ = 2500 µWb/(At·m). What is the reluctance S = l / (μ * A)?

Introduction / Context:
Reluctance in magnetic circuits is analogous to resistance in electric circuits. It quantifies the opposition to establishing magnetic flux and depends on geometry and permeability. Accurately converting units and applying S = l / (μ * A) is a common design step for transformers, inductors, and magnetic sensors.

Given Data / Assumptions:

• Length l = 0.045 m.
• Area A = 0.015 m².
• Permeability μ = 2500 µWb/(At·m) = 2500 × 10^-6 Wb/(At·m) = 0.0025 Wb/(At·m).
• Uniform cross-section and material; fringing neglected.

Concept / Approach:
Magnetic reluctance is S = l / (μ * A). Units check: l in m; μ in Wb/(At·m); A in m². Then μ * A is Wb/At, and l divided by that yields At/Wb, the correct unit for reluctance.

Step-by-Step Solution:
Convert permeability: μ = 2500 µWb/(At·m) = 0.0025 Wb/(At·m).Compute μ * A: 0.0025 * 0.015 = 0.0000375 Wb/At.Reluctance S = l / (μ * A) = 0.045 / 0.0000375 = 1200 At/Wb.Therefore, S = 1200 At/Wb.

Verification / Alternative check:
Order-of-magnitude sanity: Shorter length or larger area should reduce S; here l is modest and A is not huge, giving a mid-range S around 10^3 At/Wb, which is reasonable.

Why Other Options Are Wrong:
833.33 µAt/Wb: wrong magnitude and unit prefix; result must be in At/Wb, not micro-At/Wb.0.27 At/Wb: inconsistent with computed μ * A.More information needed: not true; formula has all required quantities.

Common Pitfalls:
Mishandling micro (µ) conversions or mixing area units; always convert µWb to Wb before calculation.

Final Answer:
1200 At/Wb