Eddy-Current Loss vs Frequency in Magnetic Cores How does eddy-current power loss in a homogeneous magnetic core vary with excitation frequency (keeping other factors like peak flux density and thickness comparable)?

Introduction / Context:
Eddy currents are circulating currents induced in conducting cores by time-varying magnetic flux. They cause I^2R losses and heating, reducing efficiency in transformers, motors, and inductors. Understanding their frequency dependence guides core material selection and lamination strategies.

Given Data / Assumptions:

• Uniform sheet/lamination of thickness t and resistivity ρ.
• Sinusoidal excitation; peak flux density Bmax considered comparable.
• Classical eddy-current loss model applies.

Concept / Approach:

The classical expression for eddy-current loss density is Pe ∝ (Bmax^2) * (f^2) * (t^2) / ρ. Thus, with Bmax, t, and ρ fixed, eddy-current loss scales with the square of frequency. This is why thin laminations, high-resistivity ferrites, or powder cores (with distributed air gaps) are used at higher frequencies to suppress eddy currents.

Step-by-Step Solution:

Verification / Alternative check:

Core loss charts separate hysteresis (∝ f) and eddy-current (∝ f^2) components; measured total loss fits Steinmetz-like models combining both contributions.

Why Other Options Are Wrong:

• Linear, cubic, or inverse dependences do not match the classical result.
• Frequency independence contradicts Faraday’s law and induced emf scaling with f.

Common Pitfalls:

Confusing total core loss (which includes hysteresis and anomalous loss) with the eddy-current component alone; ignoring the role of lamination thickness.

Final Answer:

Proportional to (frequency)^2