Compute flux density from flux and area A magnetic field has total flux Φ = 3000 µWb through a uniform cross-sectional area A = 0.25 m². What is the flux density B = Φ / A (expressed conveniently)?

Introduction / Context:
Flux density B expresses magnetic flux per unit area and is central to transformer core sizing and inductor design. Converting micro-webers to webers and presenting B in a convenient unit (tesla, millitesla, or microtesla) is a routine calculation in magnetics problems.

Given Data / Assumptions:

• Total flux Φ = 3000 µWb = 3000 × 10^-6 Wb = 0.003 Wb.
• Area A = 0.25 m².
• Uniform flux distribution across the stated area.

Concept / Approach:
Use B = Φ / A. The SI unit of B is tesla (T) = Wb/m². After computing B in tesla, convert to practical subunits if needed to match answer formatting.

Step-by-Step Solution:
Convert flux: Φ = 0.003 Wb.Compute: B = Φ / A = 0.003 / 0.25 = 0.012 T.Convert: 0.012 T = 12 mT = 12,000 µT.Therefore, B = 12,000 µT.

Verification / Alternative check:
Dimensional check: Wb/m² yields tesla; numerical scale is reasonable for modest lab magnets or transformer cores below saturation.

Why Other Options Are Wrong:
83,330 T: astronomically high; likely a unit misconversion.0 T: incorrect unless Φ = 0.More information needed: not required—Φ and A fully determine B.

Common Pitfalls:
Forgetting to convert µWb to Wb or misplacing decimal points when expressing results in µT or mT.

Final Answer:
12,000 µT