Question 1.25: Estimate the relative permeability of cast steel (see Fig. 1...
Estimate the relative permeability of cast steel (see Fig. 1.18) at (a) a flux density of 0.6 T and (b) a flux density of 1.6 T.
From Fig. 1.18, the slope of the graph at any point gives the value of μ at that point. We can easily find the slope by constructing a tangent at the point in question and then finding the ratio of vertical change to horizontal change.
(a) The slope of the graph at 0.6 T is 0.6/800 = 0.75 × 10^{−3}
Since μ = μ_0 × μ_r , μ_r = μ / μ_0 = 0.75 × 10^{−3} / 12.57 × 10^{−7}, thus μ_r = 597 at 0.6 T.
(b) The slope of the graph at 1.6 T is 0.2/4,000 = 0.05 × 10^{−3}
Since μ = μ_0 × μ_r , μ_r = μ / μ_0 = 0.05 × 10^{−3} / 12.57 × 10^{−7}, thus μ_r = 39.8 at 1.6 T.
NB: This example clearly shows the effect of saturation on the permeability of a magnetic material!