The grain-oriented silicon steel of the worked example ( , ) is to be used in a…

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Magnetic materials · Electromagnetic induction and alternating-current circuits

The Boundary-Value Problem, Ch The quasi-static approximation, eddy currents and the skin effect

Problem

The grain-oriented silicon steel of the worked example (

\sigma = 2.0\times10^6\,\mathrm{S\,m^{-1}}

\mu_r = 5000

) is to be used in a

400\,\mathrm{Hz}

transformer at the same peak field

B_0 = 1.5\,\mathrm{T}

. At

50\,\mathrm{Hz}

its

0.35\,\mathrm{mm}

sheets lose

2.3\,\mathrm{kW\,m^{-3}}

to eddy currents and

2.0\,\mathrm{kW\,m^{-3}}

to hysteresis. ((a)) Show that the ratio of eddy-current to hysteresis loss per unit volume is proportional to

fd^2

, and find the sheet thickness

d

that gives the same ratio at

400\,\mathrm{Hz}

as the

0.35\,\mathrm{mm}

sheets give at

50\,\mathrm{Hz}

. ((b)) Find the skin depth at

400\,\mathrm{Hz}

and the ratio

d/\delta

for the new sheets, and say whether the thin-sheet formula still applies. ((c)) Find the total core loss per unit volume at

400\,\mathrm{Hz}

with the new sheets, and compare it with the

0.35\,\mathrm{mm}

sheets at the same frequency.

Related theory

Magnetic materials

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