Flux density calculation in magnetics: Given a magnetic flux of 9 µWb uniformly distributed through a cross-sectional area of 5 × 10^–3 m^2, compute the flux density B and choose the correct value.

Introduction / Context:Flux density B quantifies how much magnetic flux passes through a given area and is crucial for core design, sensor calibration, and avoiding saturation in magnetic components. This problem practices converting micro-units and applying the fundamental relation B = phi / A.

Given Data / Assumptions:

• Total flux, phi = 9 µWb = 9 × 10^–6 Wb.
• Area, A = 5 × 10^–3 m^2.
• Uniform flux distribution across the stated area.

Concept / Approach:The definition of flux density is B = phi / A. After computing in SI units (Wb and m^2), express the result in tesla and convert to more convenient microtesla if appropriate. Careful unit handling prevents order-of-magnitude mistakes.

Step-by-Step Solution:

Verification / Alternative check:Check magnitude: Micro-webers over milli-square-meters gives milli-tesla range, which matches 1.8 mT. Unit consistency confirms the calculation.

Why Other Options Are Wrong:

• 555.56 T: Off by orders of magnitude; would require enormous flux or tiny area.
• 9 µT: Would correspond to 9 × 10^–6 Wb spread over 1 m^2, not 5 × 10^–3 m^2.
• 5 × 10^–3 T: Equals 5 mT, not supported by the numbers.

Common Pitfalls:Mishandling micro (10^–6) and milli (10^–3) prefixes; forgetting to divide by area; mixing up webers and tesla definitions.

Final Answer:1800 µT