Difficulty: Easy
Correct Answer: a tesla
Explanation:
Introduction / Context:
Magnetic flux density, commonly denoted by B, quantifies how much magnetic flux passes through a given area. It is central to the analysis of transformers, electric machines, magnetic sensing, and electromagnetic compatibility. Using the correct SI unit avoids confusion when converting between systems such as SI (International System) and cgs (centimeter–gram–second) units.
Given Data / Assumptions:
Concept / Approach:
Magnetic flux density B is defined as magnetic flux Φ per unit area A: B = Φ / A. In SI, magnetic flux Φ is measured in webers (Wb), and area is in square meters (m^2). Therefore, the SI unit of B is Wb/m^2. This compound unit is named the tesla (T). The cgs unit gauss (G) is sometimes encountered; 1 T equals 10,000 G, but gauss is not an SI unit. Magnetomotive force (measured in ampere-turns) and flux (measured in webers) are different physical quantities.
Step-by-Step Solution:
Identify the physical quantity: B = magnetic flux density.Identify base relation: B = Φ / A (flux per unit area).Insert SI units: Φ in webers (Wb), A in m^2 → B in Wb/m^2.Recognize derived SI name: 1 Wb/m^2 is defined as 1 tesla (T).
Verification / Alternative check:
Check dimensional consistency: a tesla also equals newton per ampere-meter (N/(A·m)), consistent with Lorentz force F = B * I * l for a conductor in a magnetic field. This confirms that tesla is the correct SI unit for B.
Why Other Options Are Wrong:
Magnetomotive force (MMF) is measured in ampere-turns, not a unit of B.
A weber is a unit of flux Φ, not flux density B.
A maxwell is a cgs unit of flux (1 maxwell = 10^-8 Wb), not B.
Gauss is a cgs unit of B, not SI.
Common Pitfalls:
Mixing cgs and SI units or treating flux (Wb) and flux density (T) as interchangeable. Always specify whether a value refers to Φ or B to avoid calculation errors.
Final Answer:
a tesla
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