Flux density change with area: If the magnetic flux remains constant but the cross-sectional area of the field region increases, how does the flux density B change?

Introduction / Context:
Flux density is a spatial measure of magnetic flux distribution. This question probes the relationship between total flux (Φ), cross-sectional area (A), and flux density (B) in magnetics design and analysis.

Given Data / Assumptions:

• Total magnetic flux Φ is constant.
• Cross-sectional area A increases.
• Uniform flux distribution over area for simplicity.

Concept / Approach:
Flux density is defined as B = Φ / A for a uniformly distributed flux. With Φ held constant, B is inversely proportional to A. Hence, when A increases, B must decrease to keep the product B * A equal to Φ.

Step-by-Step Solution:

Verification / Alternative check:
Dimensional reasoning: Weber per square meter (Wb/m^2) falls as the area denominator grows, consistent with field lines spreading out over a larger cross-section. Practical example: widening an air gap area reduces B if the same magnet produces the same Φ.

Why Other Options Are Wrong:

• Increases/Doubles: Would require Φ to rise proportionally, not true here.
• Remains the same: Only possible if Φ increases exactly with A, which contradicts the given condition.

Common Pitfalls:

• Confusing flux Φ (total lines) with flux density B (lines per unit area).
• Assuming nonuniform distributions; while real cores can be nonuniform, the inverse relation holds locally.

Final Answer:
decreases